Coursebooks

Numerical integration of stochastic differential equations

Abdulle Assyr

English

Summary

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

Content

Introduction to stochastic processes

Ito calculus and stochastic differential equations

Numerical methods for stochastic differential equations (strong and weak convergence, stability, etc.)

Stochastic simulations and multi-level Monte-Carlo methods

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 (in case of failure the second exam will be an oral 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.

Supervision

 Office hours Yes Assistants Yes Forum No

Resources

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.

In the programs

• Mathematics - master program, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Numerical integration of stochastic differential equations
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Numerical integration of stochastic differential equations
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Numerical integration of stochastic differential equations
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Computational science and Engineering, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Numerical integration of stochastic differential equations
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Computational science and Engineering, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Numerical integration of stochastic differential equations
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Financial engineering, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Numerical integration of stochastic differential equations
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Financial engineering, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Numerical integration of stochastic differential equations
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction
Lecture
Exercise, TP
Project, other

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• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German