Stochastic Differential Equations

Lectured by Paul Hager and Huilin Zhang.

  • Lectures: 
    • Starting from 17.10.23
    • Di. 15:00 bis 17:00 in 3.008 (RUD25)
    • Mi. 09:00 bis 11:00 in 3.008 (RUD25)
  • Exercise:
    • Starting from 25.10.23
    • Mi. 13:00 bis 15:00 in 1.011 (RUD25)

Course overview

This advanced course will give an introduction to stochastic differential equations (SDEs) and its relatives, with an extended part on backward stochastic differential equations (BSDEs). Specifically, we will cover the following topics:

  • Part I - SDEs
    1. Recap of Stochastic Integration
    2. Examples of SDEs
    3. Semimartingale Equations
    4. Diffusion Equations
    5. Numerical Methods
    6. Further Types of SDEs
  • Part II - BSDEs
    1. Motivation and introduction
    2. Well-posedness and basic properties
    3. Relation with PDEs—nonlinear Feymann-Kac formula
    4. Forward-Backward systems 
    5. Different kinds of BSDEs and applications
    6. Numerics Methods for BSDEs


Strong knowledge of probability is necessary and it is recommended to already be familiar with stochastic calculus.


  • Karatzas, Ioannis, and Steven Shreve. Brownian Motion and Stochastic Calculus. New York, Springer, 2014.
  • Protter, Philip E. Stochastic Integration and Differential Equations. Vol. 21. Springer Berlin / Heidelberg, 2013.
  • Øksendal, Bernt. Stochastic Differential Equations An Introduction with Applications. Berlin, Heidelberg, 2003.
  • Jianfeng Zhang. Backward Stochastic Differential Equations, From Linear to Fully Nonlinear Theory. New York, Springer, 2017.