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, Itô'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

Time	Room	Assistant	Students (last name)
Fri. 08-09	HG G 26.5	Zhouyi Tan	Ahm -- Hou
Fri. 09-10	HG G 26.5	Matti Kiiski	Hub -- Pro
Fri. 12-13	HG G 26.5	Yilin 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.