Numerical Methods in Stochastic Processes
Course: Numerical Methods in Stochastic Processes
Code: 3ФЕИТ08021
ECTS points: 6 ЕКТС
Number of classes per week: 3+0+0+3
Lecturer: Prof. Dr. Sonja Gegovska - Zajkova
Course Goals (acquired competencies): After completing this course, student should be able to analyze the convergence and the stability properties of stochastic numerical methods, to implement numerical methods for solving stochastic differential equations, to identify and understand the mathematical modeling of stochastic processes, and choose an appropriate numerical method to solve stochastic differential equations.
Course Syllabus: Strong numerical approximations for stochastic differential equations: Galerkin approximations, Euler–Maruyama and Milstein approximations. Noise approximations. Week approximation. Mild-Ito formula. Stochastic simulations and multi-level Monte-Carlo methods.
Literature:
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Required Literature |
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No. |
Author |
Title |
Publisher |
Year |
|
1 |
Raúl Toral, Pere Colet |
Stochastic Numerical Methods: An Introduction for Students and Scientists |
John Wiley & Sons-VCH |
2014 |
|
2 |
P.E. Kloeden and E. Platen |
Numerical Solution of Stochastic Differential Equations |
Springer Verlag |
1999 |
|
3 |
G.N. Milstein, M.V. Tretyakov |
Stochastic Numerics for Mathematical Physics |
Springer |
2004 |
