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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. Martin Schweizer
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)“.
VVZ CR n/a

Last Updated: 2026-02-05 16:07:27

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

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.

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)

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: In addition to the 401-....-DRL course units, adapted versions for doctoral students of the following course units: 263-4400-00L Advanced Graph Algorithms and Optimization 401-3902-21L Network & Integer Optimization: From Theory to Application 401-3904-22L Convex Optimization 401-3629-00L Quantitative Risk Management 401-3652-00L Numerical Methods for Hyperbolic Partial Differential Equations 151-0530-00L Nonlinear Dynamics and Chaos II 227-0434-10L Mathematics of Information 401-4490-22L Topology Optimization of Engineering Systems ... (continued ))