MATH-450 / 5 credits

Language: 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

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.

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional
• Semester: Spring
• Exam form: Written (summer session)
• 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
• Type: optional

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