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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
1. Real Variable.
A. Operations on sets and logical statements.
B. Fundamental inequalities.
C. Function spaces.
D. Measure theory.
E. Various types of convergence.
F. Signed measures. Absolutely continuous and singular measures. Radon-Nikodym theorem.
G. Lebesgue differentiation theorem.
H. Fubini theorem.
I. Arzela-Ascoli compactness theorem.
J. Partial ordering and maximal principle.
K. Taylor decomposition.
2. Laws of large numbers.
3. Characteristic function.
4. Central limit theorem (CLT) II.
5. Random walk.
6. Conditional probability II.
7. Martingales and stopping times.
8. Markov process.
9. Levy process.
10. Weak derivative. Fundamental solution. Calculus of distributions.
11. Functional Analysis.
12. Fourier analysis.
13. Sobolev spaces.
14. Elliptic PDE.
15. Parabolic PDE.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Function spaces.


his section lists some common notations.

$U$ is an open subset of $\QTR{cal}{R}^{n}$ . $\partial U$ is the boundary of $U$ . $\bar{U}$ is the closure of $U$ .

MATH .

MATH

MATH .

MATH .

MATH .

MATH .

MATH .

MATH .

MATH .

MATH

MATH

For a function MATH we denote

MATH (ess sup definition)
where the $\mu$ is the Lebesgue measure (see the proposition ( Existence of Lebesgue measure )).

MATH ,

MATH

MATH

MATH .

MATH , MATH

MATH is the "Schwartz space" of infinitely differentiable functions $f$ such that for any polynomial $p$ of finite dimension and any multi-index $\alpha$ we have

MATH (Schwartz space)





Notation. Index. Contents.


















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