Fiches de cours 2017-2018

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Numerical integration of stochastic differential equations

MATH-450

Enseignant(s) :

Abdulle Assyr

Langue:

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:

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

Ressources en bibliothèque
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.

 

Websites

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
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     
En construction
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand