Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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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.
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.
A. Weak convergence in Banach space.
B. Representation theorems in Hilbert space.
C. Fredholm alternative.
D. Spectrum of compact and symmetric operator.
E. Fixed point theorem.
F. Interpolation of Hilbert spaces.
G. Tensor product of Hilbert spaces.
12. Fourier analysis.
13. Sobolev spaces.
14. Elliptic PDE.
15. Parabolic PDE.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Spectrum of compact and symmetric operator.


(Spectrum of compact operator) Let $H$ be a Hilbert space, $\dim H=\infty$ and $K:H\rightarrow H$ is a linear compact operator. Then

1. MATH .


3. Either MATH is finite or it is a sequence converging to 0.


(Eigenvalues of compact symmetric operator) Let $H$ be a separable Hilbert space and $K:H\rightarrow H$ is a linear compact operator. Then there exists a countable orthonormal basis of $H$ consisting of eigenvectors of $K$ .

Notation. Index. Contents.

Copyright 2007