**Introduction to Stochastic Analysis WS 2022/23 (V3F2/F4F1)**

## Prof. Dr. Anton Bovier

### Florian Kreten

Times: | Tuesday 8-10, CP1-HSZ / Hörsaal 7 |

Friday 10-12, CP1-HSZ / Hörsaal 7 | |

Start: | 11.10.2022 |

**Content**

This course gives an introduction to the theory of stochastic analysis.

The following key concepts are covered:

- Continuous time martingales
- Brownian motion
- Stochastic integrals
- Stochastic differential equations
- Dirichlet problems

**Exercise Sheets**

You should submit your solutions in groups of two or three people. You should submit electronically via ecampus. For being admitted to the exam, you need at least 50% of all points on sheets 1-11.

Sheet 0

Sheet 1

Sheet 2

Sheet 3

Sheet 4

Sheet 5

Sheet 6

Sheet 7

Sheet 8

Sheet 9

Sheet 10

Sheet 11

Sheet 12

**Tutorials**

Tutorials take place in person at the Mathematical Institute, Endenicher Allee 60, room 1.007.

1) Mo 12-14: Alexander Becker

2) Mo 16-18: Mieszko Komisarczyk

3) Tue 12-14: Hasan Sami Tuna

### Exams

NOTE: We added one more day to have more timeslots for the oral exams in February: 07.02., 08.02., 13.02., 14.02., 15.02.. More infos in the lecture on January 13, we will then open the registration via ecampus.

The tentative dates for the second oral exams are March 20 and 21.

If possible, attend the exams in February. However, you can also skip your first examination (it will be graded as a failure), and only participate in March. In this case, write an email to florian.kreten@uni-bonn.de

### Organization

Please register for the course on ecampus. There, we manage the exercise classes, and you can also access the videos of the very same lecture from two years ago.

On basis, there is a malfunctioning link to the exercise classes on ecampus, we are not able to change this due to problems with the servers. The only important ecampus homepage is linked above.

If you want to participate in the exams, you need to register on basis *for both the exercise classes and the lecture*.

If you have any questions regarding the organization of the lecture, write an email to florian.kreten@uni-bonn.de.

### Prerequisites

Before attending the lecture, you should have spent some time studying the topics covered in Stochastic Processes.

The course builds on the lectures "Einführung in die Wahrscheinlichkeitstheorie" and "Stochastic processes". Lecture notes for both courses and more are available here. You are expected to have a reasonable knowledge of measure theory, know what conditional expectations are, have seen the construction of stochastic processes through the Daniell-Kolmogorov theorem, know key properties of martingales in discrete time, stopping times, and Markov processes. The course is suitable for advanced Bachelor students (V3F2) and for beginning Master students as a foundations module (F4F1).

### Literature

Lecture notes are available. Minor updates might follow. Please report any errors you might notice. For further reading, see the references given there.