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, Stochastic processes (or equivalent), Stochastic calculus

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
• Illustrate models based on stochastic differential equations
• Manipulate Ito calculus to be able to perfom computations with stochastic differential equations
• Choose an appropriate numerical method to solve a stochastic differential equation

Teaching methods

Ex cathedra lecture, exercises in classroom   and computer lab

Assessment methods

Mini-project + written exam

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
• Numerical Solution of Stochastic Differential Equations / Kloeden
• Stochastic Numerics for Mathematical Physics / Milstein
• An Introduction to Stochastic Differential Equations / Evans

Notes/Handbook

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

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

D. Higham, P. Kloeden, "An Introduction to the Numerical Simulation of Stochastic Differential Equations", SIAM 2021

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

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

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

Moodle Link

• https://go.epfl.ch/MATH-450