Brownian Motion and Stochastic Calculus Spring 2021

THIS IS THE PUBLIC ACCESS WEBSITE OF THE COURSE.

HERE IS THE LINK TO THE RESTRICTED ACCESS WEBSITE OF THE COURSE. Log in with your ETH ID and password - access is restricted to those students who are enrolled in the course.

Lecturer: Wendelin Werner
Coordinator and assistant: Matthis Lehmkuehler
Teaching assistant: Harprit Singh

Content

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. See for instance:

Probability Essentials by J. Jacod, P. Protter (Springer, 2004)
Probability: Theory and Examples by R. Durrett (Cambridge University Press, 2019)

Format

Until the easter break (at least), this course will be delivered online.

Each week, the following material will be posted on the restricted access website:

Lectures in mp4 format (recording of a live blackboard lecture).
Lecture Notes as a PDF.
Exercise sheets.
A written correction in pdf of the exercise sheet of the previous week.
A video correction of the exercise sheet of the previous week in mp4 format.

Also, there will be some live sessions on Zoom, not recorded:

For the corrections of the exercise sheets on Fridays.
An 'open office' time each week (via Zoom) where students can interact ‘live’ with (in alternance) the lecturer or one of the two assistants.

Finally, there is a Forum were questions about the course can be discussed.

LINKS TO ALL THIS CAN BE FOUND ON THE THE RESTRICTED ACCESS WEBSITE OF THE COURSE. Log in with your ETH ID and password - access is restricted to those students who are enrolled in the course.

Literature

The following is a selection of excellent books on the subject.

Brownian Motion, Martingales, and Stochastic Calculus by J. - F. Le Gall (Springer, 2016)
Brownian Motion and Stochastic Calculus by I. Karatzas, S. Shreve (Springer, 1998)
Continuous Martingales and Brownian Motion by D. Revuz, M. Yor (Springer, 2005)
Diffusions, Markov Processes and Martingales, volume 1 by L. C. G. Rogers, D. Williams (Cambridge University Press, 2000)
Diffusions, Markov Processes and Martingales, volume 2 by L. C. G. Rogers, D. Williams (Cambridge University Press, 2000)
Multidimensional Diffusion Processes by D. W. Stroock, S. R. S. Varadhan (Springer, 2006)