Stochastic Differential Equations

Course guarantor:

Michal Beneš

Lecturer:

Michal Beneš

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The class is devoted to an introduction to stochastic differential equations and their applications. The content includes

stochastic processes, Itô integral and solution of stochastic differential equations. The applications in filtering, diffusion

and optimal control are mentioned as well.

Requirements:

Syllabus of lectures:

1. Stochastic analogue of differential equations

2. Motivating examples

3. Probability spaces and stochastic processes

4. Itô integrals and formula

5. Representation theorem

6. Solution of stochastic differential equations

7. Problems of filtering and diffusion

8. Applications in optimálcontrol and Hamilton-Jacobi-Bellman equation

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] Øksendal B. Stochastic Differential Equations, An Introduction with Applications, Springer Verlag, Heidelberg 2003

[2] Evans L. C. An Introduction to Stochastic Differential Equations , American Mathematical Society, Boston 2014

Recommended references:

[6] Panik M. J. Stochastic Differential Equations, John Wiley & Sons, New York, 2017

[7] Liu W. Stochastic Partial Differential Equations: An Introduction, Springer Verlag, Heidelberg 2015

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikované matematicko-stochastické metody (elective course)
• Matematické inženýrství (compulsory elective course)