# Brownian Motion and Stochastic Calculus Spring 2019

Lecturer
Wendelin Werner
Coordinators
Zhouyi Tan
Lectures
Wed. 08-10 @ HG G 3
Thu. 10-12 @ HG D 7.2
First lecture
Wed. 20.02.2019
First exercise class
Fri. 22.02.2019
Course Catalogue
401-3642-00L Brownian Motion and Stochastic Calculus

[24.05.2019] Solution 12 posted. Enjoy the summer!

[24.05.2019] Solution 11 posted.

[23.05.2019] Exercise sheet 12 posted.

[21.05.2019] Solution 10 posted.

[16.05.2019] Exercise sheet 11 posted, Solution 9 posted.

[09.05.2019] Exercise sheet 10 posted.

[02.05.2019] Exercise sheet 9 posted.

[28.04.2019] Solution 8 posted.

[16.04.2019] Solution 7 posted.

[11.04.2019] Exercise sheet 8 posted.

[07.04.2019] Solution 6 posted.

[04.04.2019] Exercise sheet 7 posted.

[02.04.2019] Solution 5 posted.

[02.04.2019] Solution 5 posted.

[28.03.2019] Exercise sheet 6 posted.

[24.03.2019] Solution 4 posted.

[21.03.2019] Exercise sheet 5 posted.

[15.03.2019] Solution 3 posted.

[14.03.2019] Exercise sheet 4 posted.

[11.03.2019] Solution 2 posted.

[07.03.2019] Exercise sheet 3 posted.

[02.03.2019] Solution 1 posted.

[28.02.2019] Exercise sheet 2 posted.

[21.02.2019] Lecture notes available. An email containing the password has been sent to all the enrolled students.

[20.02.2019] Exercise sheet 1 posted.

## Course abstract

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

## Prerequisites

Familiarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in

• J. Jacod, P. Protter, Probability Essentials, Springer (2004).
• R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010).

## Lecture notes

Lecture notes are available here .

Each week a new exercise sheet will be posted here before Thursday. The exercises will then be discussed during the exercise class. If you want your exercises to be corrected, please hand in your solutions the week after either during the exercise class or in your assistant's tray located in the hallway in front of HG E 65 by Thursday evening.

Exercise sheet Due by Solutions
TimeRoomAssistantStudents (last name)
Fri. 08-09HG G 26.5Zhouyi Tan Ahm -- Hou
Fri. 09-10HG G 26.5Matti Kiiski Hub -- Pro
Fri. 12-13HG G 26.5Yilin Wang Rod -- Zub
• J.-F. Le Gall: Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). Online Version via NEBIS.
• I. Karatzas, S. Shreve: Brownian Motion and Stochastic Calculus, Springer (1991). Online Version via NEBIS.
• D. Revuz, M. Yor: Continuous Martingales and Brownian Motion, Springer (2005). Online Version via NEBIS.
• L.C.G. Rogers, D. Williams: Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000).
• D.W. Stroock, S.R.S. Varadhan: Multidimensional Diffusion Processes, Springer (2006). Online Version via NEBIS.
These books are also available in the mathematics library.