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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.
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.

Fixed point theorem.


roposition

(Banach fixed point theorem) Let $X$ be a Banach space and $A$ is a mapping $A:X\rightarrow X$ with the property MATH Then there exists a unique point $x^{\ast}$ with the property MATH





Notation. Index. Contents.


















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