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401-3642-00L 9 Credits BSC , MSC D-BSSE , D-INFK , D-MATH , D-PHYS

Brownian Motion and Stochastic Calculus

Lecturers & Examiners: Prof. Dr. Yilin Wang

VVZ CR 3.2

Last Updated: 2026-06-03 00:14:12

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)

Main link
Information

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)	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

Mathematics Bachelor
- Core Courses
  - Core Courses: Applied Mathematics and Further Appl.-Oriented Fields (¬)
Physics Bachelor
- Electives
Mathematics Master
- Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  - Core Courses: Applied Mathematics and Further Appl.-Oriented Fields (¬)
Computational Biology and Bioinformatics Master (More informations at: )
- Advanced Courses (A total of 30 ECTS needs to be acquired in the Advanced Courses category. Thereof at least 16 ECTS in the Theory and 10 ECTS in the Biology category.)
  - Theory (At least 16 ECTS need to be acquired in this category.)
Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)
- Subject Specific Electives
Quantitative Finance Master (see Students in the Joint Degree Master's Programme "Quantitative Finance" must book UZH modules directly at the UZH. Those modules are not listed here.)
- Elective
  - MF (Mathematical Methods in Finance) (For possible additional course offerings see )