**Introduction to Stochastic Analysis WS 2020/21 (V3F2/F4F1)**

## Prof. Dr. Anton Bovier

### Florian Kreten

Times: | Tuesday 8-10 |

Friday 10-12 | |

Start: | 27.10.2020 |

**The Lecture will be held digitally via Zoom. Links will be published on eCampus. You need to register here**

**for the course.**

**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**

Will be uploaded here. You should submit your solutions in groups of two or three people. For being admitted to the exam, you will need at least 50% of all points (relevant are sheets 1-10).

- 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**

Registration and allocation will take place during the first week of the lecture. All exercise classes also take place via Zoom.

- Monday 8ct
- Monday 14ct
- Tuesday 14ct

**Exams**

will be oral via Zoom. Check your electronic devices and setup beforehand:

your camera and sound must be working, further make sure you have a writing tablet

or an *additional* well-arranged camera showing a sheet of paper on which you can write.

No additional devices are allowed and no prepared notes either.

Each exam takes at most one hour and starts on the hour *s.t.* .

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

Periods for the exams are

- February 15-26, 2021
- March 22,23,29,30, 2021

You have at most two attempts for passing the exam.

Only if you fail your first attempt in February will you be admitted to the second round in March.

If you want to skip the first trial, write an email to florian.kreten@uni-bonn.de.

In this case your first trail will be graded as a failure.

**The registration for the exams is closed, you should have received the schedule via email.**

### Prerequisites

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).

Before attending the lecture, you should have spent some time studying the topics covered in Stochastic Processes (the semester break is quite long). Otherwise this course will be too advanced.

### Literature

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