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401-3642-DRL 2 Credits DR D-MATH

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Brownian Motion and Stochastic Calculus

Lecturers & Examiners: Prof. Dr. Dylan Possamaï

Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.

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Last Updated: 2026-02-05 16:22:19

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, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.

Objective

Resources

Lecture Notes

Lecture notes will be distributed in class.

Literature

- J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005). - 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).

Learning Materials (Links)

Main link
Information

General Information

Language: English
Levels: DR
Frequency: Yearly recurring

Examination

Type: ungraded semester performance

To get the credit points for this course, students can either regularly hand in solutions to the exercises, which will be assessed, or pass an oral exam after the semester. For the latter, details are to be arranged directly between student and lecturer

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type	Title	Time & Place	Hours
lecture	Brownian Motion and Stochastic Calculus	Tue 08:15-10:00 (HG E 3) Thu 08:15-10:00 (HG E 3)	4 h weekly
exercise	Brownian Motion and Stochastic Calculus Groups are selected in myStudies.	Fri 08:15-09:00 (HG G 26.5) Fri 09:15-10:00 (HG G 26.5) Fri 12:15-13:00 (HG G 26.3)	1 h weekly

Offered In

Doctorate Mathematics (More Information at: )
- Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
  - Graduate School (Official website of the Zurich Graduate School in Mathematics: )