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Quantitative Analysis
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
A. Elementary definitions of wavelet analysis.
B. Haar functions.
C. Multiresolution analysis.
D. Orthonormal wavelet bases.
E. Discrete wavelet transform.
F. Construction of MRA from scaling filter or auxiliary function.
G. Consequences and conditions for vanishing moments of wavelets.
H. Existence of smooth compactly supported wavelets. Daubechies polynomials.
I. Semi-orthogonal wavelet bases.
J. Construction of (G)MRA and wavelets on an interval.
a. Adapting MRA to the interval [0,1].
b. Adapting wavelets to interval [0,1].
c. Adapting GMRA to interval [0,1].
d. Adapting dual wavelets to interval [0,1].
e. Constructing dual GMRA on [0,1] with boundary conditions.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Construction of (G)MRA and wavelets on an interval.


o far all wavelet considerations were conducted on $\QTR{cal}{R}$ . In this section we construct wavelets on an interval $\left[ a,b\right] $ while preserving approximation and orthogonality properties and construct wavelets satisfying boundary conditions.




a. Adapting MRA to the interval [0,1].
b. Adapting wavelets to interval [0,1].
c. Adapting GMRA to interval [0,1].
d. Adapting dual wavelets to interval [0,1].
e. Constructing dual GMRA on [0,1] with boundary conditions.

Notation. Index. Contents.


















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