Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Printable PDF file
I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.


1-dimensional Lagrange element
2-dimensional Lagrange element
A priory estimate for penalised solution 1
A priory estimates for Galerkin solution 1
AS convergence vs convergence in pr 1
AS convergence vs convergence in pr 2
Accelerated calculation of Gram matrix
Adapting GMRA to interval [0,1] section
Adapting MRA to the interval [0,1] section
Adapting dual wavelets to interval [0,1] section
Adapting scaling function to the interval [0,1] section
Adapting wavelet basis to arbitrary interval
Adapting wavelets to the interval [0,1] section
Adaptive approximation section
Adaptive time step for Black PDE section
Adjoint of surjection
Adjustment of scale
Affine alpha component
Affine beta component
Affine boundary conditions
Affine characteristic function 1
Affine characteristic function 2
Affine hull
Affine set
Algebraic tensor product of Hilbert spaces
Almost sure convergence
Almost sure convergence 2
AlphaK and BetaK 1
AlphaK and BetaK 2
Analytic preconditioner for Black equation
Analytical preconditioner derived from asymptotic decomposition in time
Analytical solution for mean reverting equation
Approximate toy problem
Approximation and detail operators
Approximation and detail operators 2
Approximation and detail operators 3
Approximation and detail operators 4
Approximation and detail operators section
Approximation by smooth functions
Approximation in Nitsche norm
Arzela-Ascoli compactness criterion
Asian PDE
Assumption of coercivity 1
Asymptotic expansion for Black equation section
Asymptotic expansion of Laplace integral
Asymptotic expansion of Laplace integral section
Asymptotic expansions chapter
Asymptotic of generic Laplace integral
Asymptotic of integral with Gaussian kernel
Average difference lemma
Averaged Taylor polynomial
Averaged Taylor polynomial section
Backward Euler convergence 2
Backward Euler problem
Backward Kolmogorov PDE
Backward Kolmogorov PDE setup
Backward Kolmogorov equation
Backward Kolmogorov for Feller process
Backward Kolmogorov for discounted payoff
Backward Kolmogorov for running payoff
Backward Kolmogorov generator
Backward Kolmogorov with localization
Backward Kolmogorov with running payoff
Backward discontinuous Galerkin time-discretization
Backward induction
Backward propagator
Banach fixed point theorem
Banach space
Basic Math II part
Basic coherence condition
Basic existence of incomplete market pricing
Basic existence result
Basic properties of Fourier transform
Basic properties of conditional expectation
Basic properties of propagator 1
Basic properties of propagator 2
Basic property of orthogonal polynomials
Basis in Hilbert space
Basket credt derivative section
Bellman equation section
Bernstein inequality for wavelets
Bessel equality
BetaK separation of random walk
Bilinear form B
Bilinear form B 2
Biorthogonal QMF conditions
Biorthogonal QMF property 1
Biorthogonal QMF property 2
Biorthogonal scaling functions
Biorthogonal symmetry 1
Biorthogonal symmetry 2
Biorthogonal symmetry 3
Biorthogonality criteria 1
Black Scholes formula
Black Scholes property 1
Black final payoff plot
Black solution plot
Bond SDE
Borel measurable function
Borell-Cantelli's lemma, part 1
Borell-Cantelli's lemma, part 2
Boundary elliptic regularity
Boundedness of adjoint of surjection
Boundedness of interpolation operator
Boundedness of surjection
Bounds of interpolation error section
Box-Muller procedure
Bramble-Hilbert lemma
C to W1p estimate
C0gamma vs W1p estimate
Calculation of approximation spaces chapter
Calculation of approximation spaces in one dimension. Take two.
Calculation of biorthogonal wavelets section
Calculation of boundary scaling functions
Calculation of boundary scaling functions section
Calculation of boundary wavelets
Calculation of partial sums
Calculation of partial sums in parallel section
Calculation of scalar product in N dim
Calculation of scaling functions section
Calculation of w1 for a positive section
Calculation of w2 for a positive section
Calculation of w3 for a positive section
Calculational Linear Algebra chapter
Calculus behind the PiecewisePoly project section
Calculus behind the poly module section
Caratheodory theorem
Caratheodory theorem remark figure
Cascade algorithm
Cauchy inequality
Cauchy inequality for scalar product 1
Cauchy inequality for scalar product 2
Cauchy inequality for scalar product section
Cauchy inequality with epsilon
Central limit theorem
Central limit theorem (CLT) II section
Cg to W1p estimate
Ch.f. of a sum
Change of numeraire kernel
Changing scale of wavelet basis
Characterisation of H-tilde spaces
Characteristic exponent of a pm
Characteristic function chapter
Characteristic measure of Poisson point process
Chebyshev inequality
Chebyshev polynomials
Chebyshev polynomials calculation
Chebyshev polynomials orthogonality
Chebyshev polynomials section
Chf of entrance time 1
Chi squared distribution section
Choice of interval
Choosing probing functions section
Chunkiness parameter
Class D_T
Closedness and recession figure
Closeness and lower semicontinuity
Coefficients a
Coefficients of quadrature rule
Coherent measure
Common shape identification
Compactly supported scaling function
Compactly supported smooth biorthogonal wavelets section
Complementary slackness
Complete measure space
Complete normed space
Complete tensor product of Hilbert spaces
Completion of measure via addition of null sets
Condition number
Conditional expectation
Conditional probability chapter
Conjugate directions
Conjugate duality theorem
Conjugate gradient residue selection
Conjugate gradients
Connection between SLA and minimization
Constant finite element
Constraint qualification 1
Constraint qualification 2
Constraint qualification 3
Constraint qualification 4
Constraint qualification 5
Constructing dual GMRA on 01 with boundary conditions section
Constructing maximum summary
Construction of MRA and wavelets on half line or an interval section
Construction of MRA section
Construction of approximation spaces section
Construction of generic Levy process
Construction of symmetric biorthogonal wavelets
Continuity lemma
Continuity point
Convergence in Lp and in probability 1
Convergence in Lp and in probability 2
Convergence lemma for family of complex numbers
Convergence of cascade procedure section
Convergence of conjugate gradient method
Convergence of discontinuous Galerkin technique
Convergence of finite elements for generic parabolic operator section
Convergence of modified cascade procedure section
Convergence of pm and chf 1
Convergence of pm and chf 2
Convergence of product
Convergence theorem for martingales
Conversion of representations
Convex Hull Cone Relative Interior
Convex and proper function
Convex function picture
Convex homogenous function property
Convex hull
Convex set
Convexity of partial minimum
Convolution and smoothing section
Convolution of polynomials 1
Convolution of polynomials 2
Convolution of polynomials 3
Convolution of polynomials 4
Corrected difference 2 figure
Corrected difference figure
Crank-Nicolson convergence for heat equation
Crank-Nicolson problem for heat equation
Credit risk figure 1
Credit risk figure 2
Credit risk figure 3
Criteria of positive definiteness
Crossing points figure 1
Crossing points figure 2
Crossing points figure 3
Crossing theorem 1
Crossing theorem 2
Crossing theorem 2 figure
Crudification of piecewise-quadratic representation
Crudification operator
Crudification operator 2
Cuda and python section
Currency exchange section
Cutoff function
DHE with term structure
Data Analysis part
Decomposition of a convex set
Decomposition of payoff function in one dimension section
Definition of A_i
Definition of Epsilon
Definition of Galerkin basis 1
Definition of K0
Definition of K1
Definition of P_i
Definition of Q_i
Definition of conditional probability section
Definition of g_k
Definition of the Poisson process
Definitions and the main convergence theorem section
Delta hedging
Derivative vs scale
Deterministic optimal control problem section
Diagonal preconditioner section
Difference figure
Differential inequality 1
Differential inequality 2
Differentiating call with respect to maturity 1
Differentiating call with respect to maturity 2
Differentiation of asymptotic power series
Dimension mismatch
Dimension of tensor product
Dirac delta function
Direct Fourier transform
Direction of recession figure
Directional derivative
Directions of recession
Dirichlet problem for generic parabolic operator
Discontinuous Galerkin time-discretization
Discrete wavelet transform section
Discrete wavelet transform setup
Discretization for backward Kolmogorov equation section
Discretization with respect to time parameter section
Displaced Heston equations
Displaced Heston equations chapter
Displaced diffusion section
Dissipation property of Feller process
Distribution density via Call
Distribution of Poisson process section
Dominated convergence theorem
Dual Sobolev spaces section
Dual basis
Dual feasibility
Dual frame
Dual problem
Dual space
Dual wavelets
Dual wavelets properties
Dual wavelets section
Duality gap and geometric multipliers
Duality picture 1
Duality picture 2
Egorov theorem
Eigenfunctions of Laplacian
Eigenvalues of compact symmetric operator
Eigenvalues of symmetric elliptic operator
Elementary CLT
Elementary definitions of wavelet analysis section
Elliptic Dirichlet problem
Elliptic PDE section
Elliptic Ritz projection
Elliptic alternative 1
Elliptic alternative 2
Elliptic boundedness of inverse
Elliptic differential operator
Elliptic regularity for Poisson equation
Elliptic regularity section
Embedding of dual Sobolev space
Energy approximation
Energy estimate 2
Energy estimates for the Galerkin approximate solution
Energy estimates for the bilinear form B
Equivalence of AS and PR convergence for series
Equivalence of toy problems
Equivalent definitions of vague convergence
Equivalent sequences of rv
Error and residual
Error and residual 2
Estimate for K0
Estimate for K1 one
Estimate for K1 two
Estimate of interpolation error
Estimate of interpolation error 2
Estimate of interpolation error 3
Estimate of mean by probability series
Estimation of averaged Taylor polynomial
Euler Lagrange equation
Evaluating matrix R section
Eventuality of random walk
Evolution figure
Evolution of u
Evolution of y
Evolution with penalty term
Evolutionary penalised problem
Evolutionary variational inequalities section
Evolutionary variational inequality problem
Example Black equation parameters section
Example Black problem
Example approximate problem
Example stochastic elliptic problem
Example strong Black problem
Example strong Black problem 2
Example strong elliptic problem
Example weak elliptic problem
Existence and uniqueness for evolutionary problem
Existence and uniqueness for non-coercive stationary problem.
Existence and uniqueness for penalised problem
Existence and uniqueness for penalised problem 2
Existence and uniqueness for stationary problem
Existence for Galerkin approximation of stationary problem
Existence of Lagrange multipliers for equality constraints
Existence of Lebesgue measure
Existence of adapted wavelets
Existence of biorthogonal basis 1
Existence of biorthogonal compactly supported wavelets
Existence of conditional expectation
Existence of derivative via finite difference
Existence of incomplete market pricing
Existence of orthogonal polynomials
Existence of orthonormal wavelet bases 1
Existence of orthonormal wavelet bases 2
Existence of smooth compactly supported wavelets
Existence of subdifferential
Existence of wavelets with orthogonality across scales
Existence of weak solution for elliptic Dirichlet problem 1
Existence of weak solution for elliptic Dirichlet problem 2
Existence of weak solution for elliptic Dirichlet problem 3
Existence of weak solution for the parabolic Dirichlet problem
Existence of weak solution of the Heat equation
Existence of weak solution of the Poisson equation
Exponential change
Extension of Borell-Cantelli lemma to random walk
Extension of measure to sigma algebra
Extension theorem
Extremal properties of orthogonal polynomials
Extreme points of polyhedral set 1
Extreme points of polyhedral set 2
FJ proof 1
FJ proof 2
FJ proof 3
Fair Variance vs Log contract
Farkas lemma
Fatou lemma
Feasible direction cone
Feller process
Feller process property 1
Finite QMF convergence
Finite difference basics
Finite difference basics section
Finite difference in Sobolev space
Finite difference schemes for heat equation section
Finite differences
Finite dimensional approximation 1
Finite dimensional approximation 2
Finite element
Finite element section
Finite elements chapter
Finite elements for Poisson equation with Dirichlet boundary conditions section
Finite space variable incomplete market
First order PDE
Form of Schwarz operator
Forward Kolmogorov equation for Ito process
Forward LIBOR
Forward and backward generators def
Forward and backward generators section
Forward propagator
Fourier analysis in Hilbert space section
Fourier decomposition
Fourier series on unit interval
Fourier series section
Fourier transform
Fourier transform of convolution
Fourier transform of delta function section
Fourier transform of projection on span of translates
Fourier transform section
Frame formula 1
Frame norm
Frame operator
Frame property 1
Frame property 2
Frame property 3
Frame system
Fredholm alternative
Free boundary problem 1
Free boundary problem 2
Free boundary problem 2 summary
Friedrich lemma
Fritz John conditions
Fubini theorem
Function spaces section
Functional analysis chapter
Fundamental solution for ODE
GMRA Ries bases
Gagliardo-Nirenberg-Sobolev inequality
Galerkin approximation 1
Galerkin approximation 2
Galerkin approximation for parabolic Dirichlet problem section
Galerkin approximation of stationary problem
Galerkin coefficients
Galerkin convergence 1
Galerkin convergence 2
Galerkin convergence 3
Galerkin convergence 4
Galerkin convergence 5
Galerkin convergence 6
Galerkin problem
Gamma function primer
Gauss-Hermite Intergration
Gaussian quadrature rule
Generalized multiresolution analysis
Generator of Levy process
Generic Backward Kolmogorov
Generic Forward Kolmogorov
Generic parabolic PDE
Generic parabolic PDE problem
Generic parabolic PDE setup
Geometric multiplier
Geometric multiplier property
Gershgorin circle theorem
Girsanov theorem
Global approximation by smooth functions
Gram-Schmidt orthogonalization section
Green formula
Gyongy 2
Gyongy lemma section
H-tilde spaces
Haar functions section
Hahn decomposition theorem
Hankel determinants
Heat equation weak formulation 1
Heat equation weak formulation 2
Heat equation with Dirichlet boundary condition
Heat equation with Neumann boundary condition
Heston approximation
Hewitt and Savage zero-or-one law
High order internal elliptic regularity
Higher degree of exactness
Holder inequality
Holder inequality 2
Holder inequality 3
Holospoudic criteria
How does it extend to multiple dimensions section
Hyperplane representation
IO criteria for AS convergence
Idea of Bayesian analysis section
Identification of nodal variables 1
Identification of nodal variables 2
Implementation for mean reverting equation section
Implementation tools II part
Implicit equation with penalty term
Implicit formulation of the penalty term section
Implicit spectrum
Impossibility of backward induction section
Improving condition number
Incomplete Market 1
Incomplete Market 2
Incomplete market ask
Incomplete market bid
Independence of Poisson processes
Independency of pre-alpha and post-alpha fields
Independent process
Induced outer measure
Infimal convex function
Infimal convolution
Infimal convolution of support functions
Infinitely divisible pm
Infinitely often zero-or-one law
Instant smoothness of solution operator for PP 1
Int t_dW
Integral form of Taylor decomposition
Integral of scaling function
Integral of scaling function 2
Integral of wavelet
Integration by part for finite differences
Integration of fundamental solution for Black equation
Integration of polynomials
Interaction of approximation and detail operators with Fourier transform
Interaction of downsampling with Fourier transform
Interaction of tilde with Fourier transform
Interaction of upsampling with Fourier transform
Interpolated continuity
Interpolation inequality
Interpolation of Hilbert spaces section
Intersection of halfspaces
Intersection property
Invariant set
Inverse Fourier transform
Inversion of chf into df
Inversion of chf into pm 1
Inversion of chf into pm 2
Ito calculus
Ito calculus section
Ito formula 2
Ito isometry
Jackson inequality for wavelets
Jackson inequality for wavelets 2
Jacobi matrix
Jensen inequality
Jordan decomposition theorem
Kolmogorov equations in general setting
Kolmogorov inequality for series 1
Kolmogorov inequality for series 2
Kolmogorov three series theorem
Kolmogorov zero-or-one law
Kolmogorov-Chapman equation
Krein-Milman theorem
Kronecker summation lemma
LIBOR market model section
Lagrange interpolation formula
Lagrange interpolation formula 1
Lagrange multiplier
Lagrangian optimality
Laplace quadrature section
Laplace transform section
Law of large number for iid rv with finite mean
Law of large numbers for independent rv
Lax-Milgram theorem
Lebesgue differentiation theorem
Lebesgue differentiation theorem section.
Lebesgue integral definition
Left and right derivatives
Levy process
Levy process chapter
Levy-Khintchine formula 1
Levy-Khintchine formula 2
Liapounov CLT
Liapounov inequality
Limit points
Limsup and liminf for sets
Lindeberg-Feller CLT
Lindeberg-Feller condition
Line segment principle
Linear equation
Linear independence from biorthogonality
Linear intersection result
Linear tensor product element
Linear transformation of random variables
Local approximation by smooth functions
Local minima of convex function
Local minimum of a sum
Localised integral
Localised scaling
Localised transport
Localization for mean reverting equation section
Localization for mean reverting equation summary
Localization section
Longstaff-Schwartz technique section
Lp interpolation
Lp vs W1p estimate
MMA numeraire
Magnitude of matrix Epsilon
Main properties of direction of recession
Main property of Fourier decomposition
Main property of Haar functions 1
Main property of basis in Hilbert space
Main property of convex function
Main property of crudification operator
Manipulation of localized piecewise polynomial functions
Mapping of conditional expectation
Mapping of rv
MarkPr TargetEquation
MarkPr TargetEquations 2
MarkPr1 Beta
MarkPr1 Sigma
Market model section
Markov property
Markovian projection
Markovian projection on displaced diffusion section
Markovian projection section
Martingale definition
Martingale property of Feller process
Mathematica Test 1
Mathematica Test 1a
Mathematica Test 2
Mathematica Test 3
Matrix Lambda
Matrix V
Matrix of discontinuous Galerkin
Maximal dimension 1
Maximal inequality for martingales
Maximum of random walk
Mean reversion 0
Mean reversion 1
Mean reversion 2
Mean reversion 3
Mean reversion 4
Mean reversion 5
Mean reverting equation section
Mean reverting free boundary problem
Mean reverting free boundary problem 2
Mean reverting problem
Mean reverting problem 2
Mean reverting solution
Measurable set
Measurable space
Method of conjugate directions section
Method of conjugate gradients section
Method of steepest descent section
Min common and max crossing point section
Minimax equality
Minimax lemma 1
Minimax lemma 2
Minimax theorem
Minimax theorem 1
Minimization with equality constraints
Minimum norm optimality of Chebyshev polynomials
Minimum of a convex function
Minimum of a smooth function
Minkowski-Weyl representation
Minkowski-Weyl theorem
Mix of backward induction and penalty term approaches I. Implementation and results section
Mix of backward induction and penalty term approaches II section
Mix of backward induction and penalty term approaches section
Mix2 figure 1
Mix2 figure 2
Mix2 figure 3
Mix2 figure 4
Modified cascade procedure
Mollifier for a ball 1
Mollifier for a ball 2
Monotonicity of solution of stationary problem
Morrey inequality
Multidimensional Gyongy lemma
Multidimensional backward Kolmogorov equation
Multiplication of polynomials
Multiresolution analysis
Multiresolution analysis section
N-dim test 1
Necessary and sufficient optimality conditions
Nitsche bilinear form
Nitsche form energy estimates
No drift Black Scholes
Non emptiness of relative interior
Non-coercivity assumption 1
Nondecreasing ratio
Nonvertical separation
Nonvertical separation figure
Normal cone
Normal cone figure 1
Normal distribution with unknown parameters 1
Normal distribution with unknown parameters 2
Notation W_d
Numerical analysis part
O symbols
OST property 0
OST property 1
OST property 2
OST property 3
One dime payoff residue figure
One dimensional problems chapter
Operations on sets and logical statements
Operator L
Operator L 2
Optimal stopping
Optimal stopping time problem section
Optimal strategy with accrual
Optimal utility section delta hedging
Optimality for smooth function figure 1
Optimality for smooth function figure 2
Optional random variable
Optional sampling theorem
Order of summation 0
Order of summation 1
Order of summation 2
Order of summation 3
Order of summation 4
Order of summation 5
Orthogonal L2 projection
Orthogonal polynomials
Orthogonality of residues
Orthogonality of residues 2
Orthonormal system of translates def
Orthonormal system of translates section
Orthonormal wavelet bases section
Orthonormal wavelet basis
Outer measure
Parabolic Dirichlet problem
Parabolic PDE section
Parabolic differential operator
Parabolic problem with nonsmooth initial condition
Parabolic regularity 1
Parabolic regularity 2
Parabolic regularity for heat equation
Parabolic regularity section
Parallel subspace correction method section
Parallel subspace preconditioner
Parallel subspace preconditioner property
Parameter averaging
Parameter averaging section
Parameter d
Parseval equality
Partial inversion lemma
Partial inversion lemma 2
Partial minimization result
Partial solution
Partial summation in parallel
Partially inverted problem
Partially inverted semidiscrete parabolic problem
Partially inverted semidiscrete parabolic problem 1
Partition of unity definition
Pathwise differentiation
Payoff figure
Penalisation error
Penalised evolutionary problem section
Penalized mean reverting problem
Penalized problem
Penalized problem for mean reverting equation section
Permutable set
Pervasive idea of recursive calculation section
Piecewise Quadratic Polynomial picture
Piecewise convolution
Piecewise linear MRA section
Piecewise polynomial representation
Piecewise polynomials in parallel
Piecewise polynomials section
Pm vs chf estimate
Poincare inequality
Poincare inequality for a ball
Poisson equation weak formulation 1
Poisson equation weak formulation 2
Poisson equation with Dirichlet boundary condition
Poisson formula for delta function
Poisson formula section
Poisson point process
Poisson point process section
Poisson process chapter
Poisson property 1
Poisson property 1a
Poisson property 2
Poisson property 3
Polar cone definition
Polar cone properties
Polar cone theorem
Polar polyhedral cone
Polyhedral function
Positive definite inner product
Possible value of random walk
Post-alpha process
Pre-alpha field
Precompactness of a tight sequence of pm
Preconditioner for Black equation in case q=1 section
Preconditioning section
Preliminary reduction
Preliminary reduction 2
Preservation of closeness result
Preservation of convexity
Preservation of stationary measure
Primal feasibility
Primal problem
Principal intersection result
Probability based criteria for AS convergence
Projection permuation
Projection theorem
Proof of existence for stationary problem section
Propagator and transitional probability
Proper separation 1
Proper separation 2
Properties of Feller resolvent 1
Properties of Feller resolvent 2
Properties of Feller resolvent 3
Properties of Poisson point process
Properties of Schwarz operator
Properties of averaged Taylor polynomial
Properties of dual frame
Properties of frame operator
Properties of interpolant
Properties of left and right derivative
Properties of mollifiers
Properties of sequences h and g
Properties of sequences h and g section
Properties of solution operator
Properties of solution operator 2
Properties of spline functions
Properties of subgradient
Property of equivalent sequences of rv
Property of scale and transport 1
Property of scale and transport 2
Property of scale and transport 3
Property of scale and transport 4
Property of scale and transport 5
Property of scale and transport 6
Property of scale and transport 7
Property of transport 1
Property of transport 2
Python to R Communicator section
Python utilities section
QMF conditions
QMF property 1
QMF property 2
QMF section
Quadratic form minimum
Quadratic intersection result
Quadratic piecewise interpolation
Quadratic piecewise interpolation 2
Quadratic polynomials 1
Quadratic polynomials 2
Quadratic polynomials 3
Quadratic polynomials 4
Quadratic polynomials 5
Quadrature rule
Quadrature rule 1
Radon-Nikodym theorem
Random walk
Random walk space
Random walk space approximation
Real valued random variable
Rebalancing wavelet basis problem
Rebalancing wavelet basis section
Recession cone of intersection
Recession cone of inverse image
Recovering MRA from auxilliary function 1
Recovering scaling function from auxilliary function section
Recurrence lemma 1
Recurrence lemma 2
Recurrence result 1
Recurrence result 2
Recurrent value of random walk
Recursive calculation
Recursive equation
Recursive relationships for wavelet section
Recursive relationships for wavelet transform
Reduction of Black equation
Reduction scheme 1
Reduction scheme 2
Reduction to system of linear algebraic equations for Black PDE section
Reduction to system of linear algebraic equations for mean reverting equation section
Reduction to system of linear algebraic equations for q=1
Reduction to system of linear algebraic equations for q=1 section
Reduction to system of linear algebraic equations for q=1 summary
Reduction to system of linear algebraic equations section
Reduction to system of linear algebraic equations summary
Reduction to well conditioned form section
Reflection principle picture
Regularity of a set
Relative interior figure
Rellich-Kondrachov compactness theorem
Remainder bound 1
Remainder of averaged Taylor polynomial
Remainder of averaged Taylor polynomial 2
Remainder of averaged Taylor polynomial 3
Remark on stability of financial problems
Remote event
Remote field
Removing stiffness from penalized equation section
Representation of dual Sobolev space
Representation of solution for elliptic PDE using stochastic process section
Reproduction of polynomials 1
Reproduction of polynomials 2
Reproduction of polynomials 3
Reproduction of polynomials 4
Resolution structure for adapted scale functions
Resolvent of Feller process
Restricted linear independence
Review of variational inequalities in maximization case section
Riesz basis
Riesz basis condition
Riesz frame
Riesz potential bound 1
Riesz potential bound 2
Riesz property
Riesz representation theorem
Risk neutral Brownian motion
Risk neutral measure via Girsanov section
Ritz projection convergence 1
Saddle point defining property
Saddle point result 1
Saddle point result 2
Saddle point theorem
Same grid reduction
Saturated measure space
Scalar product in N dimensions
Scalar product in N-dimensions Test case 2
Scale and transport operators
Scale and transport operators 2
Scale of polynomial
Scaling equation
Scaling equation 2
Scaling equation 3
Scaling equation 4
Scaling equation 5
Scaling equation for wavelet section
Scaling equation section
Scaling filter and auxiliary function
Schwartz space
Schwarz operator
Second derivative localization
Second order internal elliptic regularity
Self financing strategy
Semi-orthogonal wavelet bases section
Separable and dense set
Separating hyperplane theorem
Shift and sampling operators
Shifted Fourier transform equality
Sigma algebra
Sigma finite set
Simple function definition
Simple law of large numbers
Smooth compactly supported wavelets section
Smooth optimization problem
Smooth version of the penalty term section
Smoothness of compactly supported wavelets with vanishing moments
Smoothness of compactly supported wavelets with vanishing moments section
Sobolev conjugate
Sobolev inequality
Sobolev inequality 2
Sobolev space definition
Sobolev spaces in N dim as tensor products
Sobolev spaces section
Sobolev spaces with dominating mixed derivative
Solution operator for PP with nonsmooth IC
Solution operator for elliptic problem
Solution operator for generic elliptic problem
Solving N-dimensional PDEs section
Solving equation with implicit penalty term section
Solving one dimensional Black PDE section
Solving one dimensional mean reverting equation section
Space splitting setup
Sparse tensor product
Sparse tensor product approximation 1
Sparse tensor product approximation 2
Sparse tensor product definition section
Sparse tensor product section
Sparse tensor product setup
Spectral mapping theorem
Spectrum of compact operator
Spitzer identity
Spline functions definition
Spline functions section
Stability of general evolution equation
Stability of one-dim heat equation schemes section
Stability of splitting for Sobolev spaces with dominating mixed derivative
Stability of splitting for tensor product of Sobolev spaces
Stability of wavelet splitting 1
Stability of wavelet splitting section
Stable space splittings section
Stable splitting
Standard mollifier definition
Star shaped set
Starting scaling function
Stationary independent increments
Stationary penalised problem
Stationary variational inequality problem
Steepest descent
Stochastic optimal control section
Stochastic optimization in one dimension chapter
Stochastic optimization over wavelet basis section
Stochastic process
Stregthened Cauchy-Schwartz inequality
Stress tests
Strict hyperplane separation 1
Strict hyperplane separation 2
Strong formulation of evolutionary problem
Strong formulation of stationary problem
Strong law of large numbers for iid rv
Strong law of large numbers for mean zero
Strong mean reverting problem
Strong mean reverting problem 2
Structure of recurrent values
Subgradient and subdifferential
Subprobability measure
Subspace bases
Sufficient conditions for vanishing moments
Sufficient conditions for vanishing moments 2
Sufficient statistics for normal sample section
Sufficiently fine scale
Sufficiently fine scale 2
Summary for Black equation in case q=1
Summary for Black equation in case q=1 section
Summary for Black equation in case q=1, any time interval
Summary for Black equation in case q=1, inverted matrix
Summary for mean reverting equation in case q=1
Support function
Support of scaling function
Supporting hyperplane theorem
Swap rate
Symmetric biorthogonal wavelets section
Symmetric principal part
Symmetrization section
T-forward probability measure
Tangent cone
Tangent cone 2
Tangent cone 3
Tangent cone 4
Tangent cone figure 1
Tangent cone figure 2
Taylor decomposition in Peano form
Taylor decomposition in Schlomilch, Lagrange and Cauchy forms
Taylor polynomial
Tensor product of Hilbert spaces section
Tensor product of bounded operators
Tensor product of function spaces
Tensor product properties 1
Tensor product properties 2
Tensor product splitting
Three-term recurrence relation
Tight sequence
Time dependent elliptic problem
Time dependent elliptic variational problem
Time discretization of penalty term section
Time series forecasting section
Time-weak backward Kolmogorov
Time-weak problem
Toy approximation in energy norm
Toy problem
Trace theorem
Trace-zero functions in W1p
Transformation of SDE based on delta hedging section
Transformation of SDE under change of measure
Transformation of parabolic problem 1
Transformation of parabolic problem 2
Transition function
Transport of polynomial
Trigonometry primer
Unbounded existence result
Uniform continuity of chf
Uniform convergence
Uniform property of vague convergence
Uniformly equicontinuous sequence
Uniformly smooth approximation lemma
Union property
Uniqueness of weak solution for the parabolic Dirichlet problem
Unscented conditions for mean
Unscented covariance summary
Unscented mean section
Unscented mean summary
Unscented transformation section
Unsuitability of spline wavelets
Unsuitability of spline wavelets 2
Useful formula
V for linear MRA 0
V for linear MRA d
V0 for linear MRA
Vague convergence
Vague convergence as a weak convergence 1
Vague convergence as a weak convergence 2
Vague convergence section
Vague precompactness of spm
Vanishing moments for biorthogonal wavelets section
Vanishing moments of wavelet section
Vanishing moments vs approximation
Vanishing moments vs approximation 2
Vanishing moments vs approximation 3
Vanishing moments vs decay at infinity
Variance of target process
Variance swap pricing section
Variational Dirichlet problem for generic parabolic operator
Variational inequalities chapter
Variational inequalities in maximization case
Variational inequality example
Variational toy problem
Visualization lemma
W1p embedding
Wavelet analysis section
Wavelet approximation 1
Wavelet approximation 2
Wavelet approximation 3
Wavelet approximation 4
Wavelet calculations chapter
Wavelet estimates in Sobolev spaces section
Wavelets on 01 step 1
Weak backward Kolmogorov with respect to time
Weak compactness of bounded set
Weak derivative
Weak derivative section
Weak duality theorem
Weak formulation of stationary problem
Weak formulation with respect to time parameter
Weak formulation with respect to time parameter section
Weak maximal principle 1
Weak solution of elliptic Dirichlet problem
Weak solution of parabolic Dirichlet problem
Weierstrass theorem
Whittaker sampling theorem
Wiener-Hopf technique
X to Y connection
Young inequality
Zeros of orthogonal polynomials
Zorn maximal principle
[0,1]-adapted GMRAs
[0,1]-adapted MRA
definition of minmax p
ess sup definition
generalized impulse equation
generalized impulse solution
log contract section
operations on sets section
recovery of implied distribution
static replication formula
step function

Notation. Index. Contents.

Copyright 2007