# 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 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.

#### 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, 2020-2021, 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, 2020-2021, 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, 2020-2021, 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, 2020-2021, 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, 2020-2021, 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, 2020-2021, 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, 2020-2021, 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

### legend

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