**Stochastic Analysis SS 2023 (V4F1)**

## Prof. Dr. Anton Bovier

### Florian Kreten

Times: | Tuesday 12-14 c.t. |

Thursday 12-14 c.t. | |

Start: | 03.04.2023 |

Place: | Zeichensaal, Wegeler Strasse 10 |

**Content**

This is the second course on stochastic analysis. It will cover a selection of advanced topics. Currently, the plan is to cover:

- One-dimensional diffusions, speed measures, and the trap model
- Lévy processes
- Extreme values and Poisson point processes
- Functional limit theorems for sums of independent random variables
- Extensions to sums of dependent random variables and applications to random walks in random environments

There are preliminary lecture notes for this course which also contain references for further reading.

**Prerequisites:** The course will assume knowledge in probability theory based on the courses Stochastic Processes and Introduction to Stochastic Analysis. The material coverd in the course Markov Processes is not required.

**Organization**

You need to register for both the course* and* for the exercise classes on ecampus. If you want to attend the exams, do not forget to register on BASIS in time. For any questions regarding the organization of the lecture, write an email to florian.kreten@uni-bonn.de .

**Exercise Sheets**

Sheet 1

Sheet 2 (small update)

Sheet 3

Sheet 4

Sheet 5 (small update)

Sheet 6

Sheet 7

Sheet 8

Sheet 9

Sheet 10

Sheet 11

Sheet 12 (small update)

**Tutorials**

Begin in the second week of the lecture period. Registration will be done in the first lectures. There will be two tutorial classes:

Tuesday 16-18, 0.007 Endenicher Allee 60 (Mieszko Komisarczyk)

Friday 10-12, 0.007 Endenicher Allee 60 (Matteo Licheri)

**Evaluation:**

**The evaluation of the lecture will take place online during the lecture on Tuesday, May 23. You will then be given the access codes. You will need to bring some device with which you can log into the website and fill out the form. **

**Exams**

**You can now book your timeslot for the first oral exam on ecampus (check your two registrations on BASIS though, which are also mandatory). The registration will close on July 07.**

For the exam, you will have the *option* to select a specific topic with which to start the exam.

The dates for the first exams are July 25 & 26. The dates for the second exams are September 19 & 20.