MATH-450 / 5 crédits

Langue: Anglais

Summary

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

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.

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.

Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Numerical integration of stochastic differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Numerical integration of stochastic differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Numerical integration of stochastic differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Numerical integration of stochastic differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Numerical integration of stochastic differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Numerical integration of stochastic differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Numerical integration of stochastic differential equations
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 Lu Ma Me Je Ve 8-9 9-10 10-11 11-12 12-13 13-14 14-15 MAA112 15-16 16-17 MAA112 17-18 18-19 19-20 20-21 21-22

Lundi, 14h - 16h: Exercice, TP MAA112

Jeudi, 16h - 18h: Cours MAA112

Cours connexes

Résultats de graphsearch.epfl.ch.