Numerical integration of stochastic differential equations

Summary

In this course we will introduce and study numerical integrators for stochastic differential equations. These numerical methods are important for many applications.

Content

Learning Prerequisites

Recommended courses

Numerical Analysis, Advanced probability

Learning Outcomes

By the end of the course, the student must be able to:

• Analyze the convergence and the stability properties of stochastiques numerical methods
• Implement numerical methods for solving stochastic differential equations
• Identify and understand the mathematical modeling of stochastic processes
• Manipulate Ito calculus to be able to perfom computation with stochastic differential equations
• Choose an appropriate numerical method to solve stochastic differential equations

Teaching methods

Ex cathedra lecture, exercises in classroom    

Assessment methods

Written examination

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Resources

Ressources en bibliothèque

• Stochastic Differential Equations, Theory and applications / Arnold
• Introduction to Stochastic Integration / Kuo
• An Introduction to Stochastic Differential Equations / Evans
• Stochastic Numerics for Mathematical Physics / Milstein
• Numerical Solution of Stochastic Differential Equations / Kloeden

Notes/Handbook

L. Arnold, "Stochastic Differential Equations, Theory and applications", John Wiley & Sons, 1974

L.C. Evans, "An Introduction to Stochastic Differential Equations", AMS, 2013

P.E. Kloeden, E. Platen, "Numerical Solution of Stochastic Differential Equations", Springer, 1999. 

H-H. Kuo, "Introduction to Stochastic Integration", Springer, 2005.

G.N. Milstein, M.V. Tretyakov, "Stochastic Numerics for Mathematical Physics", Springer, 2004.

Moodle Link

• https://go.epfl.ch/MATH-450