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401-3642-00L 9 Credits BSC , MSC D-BSSE , D-INFK , D-MATH , D-PHYS
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Brownian Motion and Stochastic Calculus

Lecturers & Examiners: Prof. Dr. Martin Schweizer
VVZ CR 3.2

Last Updated: 2026-06-01 11:33:10

Abstract

This course gives an introduction to Brownian motion and stochastic calculus. It includes the construction and properties of Brownian motion, basics of Markov processes in continuous time and of Levy processes, and stochastic calculus for continuous semimartingales.

Objective

This course gives an introduction to Brownian motion and stochastic calculus. The following topics are planned: - Definition and construction of Brownian motion - Some important properties of Brownian motion - Basics of Markov processes in continuous time - Stochastic calculus, including stochastic integration for continuous semimartingales, Ito's formula, Girsanov's theorem, stochastic differential equations and connections with partial differential equations - Basics of Levy processes

Resources

Lecture Notes

Lecture notes will be made available in class.

Literature

- R.F. Bass, Stochastic Processes, Cambidge University Press (2001). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - 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).

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 20 minutes
20 minutes preparation and 20 minutes exam (one candidate prepares during the 20 minutes oral exam of the previous candidate).

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)
  • 27.02 Date 08:15-10:00 (ML D 28)
4 h weekly
exercise Brownian Motion and Stochastic Calculus
  • 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