- Lecturer
- Wendelin Werner
- Coordinator
- Matthis Lehmkuehler
- Lectures
- Online Lectures
- Course catalogue
- 401-3642-00L

This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Itô's formula and applications, stochastic differential equations and connection with partial differential equations.

Familiarity with measure-theoretic probability as in
the standard D-MATH course
**Probability Theory** will be assumed.
Below are some textbooks covering this topic.

- Probability Essentials by J. Jacod, P. Protter (Springer, 2004)
- Probability: Theory and Examples by R. Durrett (Cambridge University Press, 2019)

The lecture notes can be found here (the password will be mentioned in the first lecture).

Lectures will be recorded and published weekly on the Videoportal. The password will be communicated in an email.

Every week a new exercise sheet will be posted on this
site by **Thursday**. The exercise sheet
will be discussed in the **following week**
in the online exercise class. If you would like your work to
be corrected, submit your solutions via the
SAMUp Tool
to your assistant (you will need to use VPN to access
this site). Corrected answers will be returned via the same page.

Exercise sheet | Due by | Solutions |
---|---|---|

- | - | - |

The exercise classes by Daniel Contreras Salinas, Maximilian Nitzschner and Matthis Lehmkuehler which used to happen on Fridays at 8 a.m., 9 a.m. and 12 a.m. respectively, do not take place anymore. Instead we will upload a video to this folder each week instead (the password is the same as for the lecture notes).

To ask questions about the course content or other things related to the course, we have set up a Forum and would like to encourage you to sign up and make use of it as asking questions in the digital exercise class format is not possible.

The following is a selection of excellent books on the subject.

- Brownian Motion, Martingales, and Stochastic Calculus by J. - F. Le Gall (Springer, 2016)
- Brownian Motion and Stochastic Calculus by I. Karatzas, S. Shreve (Springer, 1998)
- Continuous Martingales and Brownian Motion by D. Revuz, M. Yor (Springer, 2005)
- Diffusions, Markov Processes and Martingales, volume 1 by L. C. G. Rogers, D. Williams (Cambridge University Press, 2000)
- Diffusions, Markov Processes and Martingales, volume 2 by L. C. G. Rogers, D. Williams (Cambridge University Press, 2000)
- Multidimensional Diffusion Processes by D. W. Stroock, S. R. S. Varadhan (Springer, 2006)

These books are also available in the mathematics library.