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401-3642-00L 10 Credits BSC , DR , MSC D-BSSE , D-INFK , D-MATH

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Brownian Motion and Stochastic Calculus

Lecturers & Examiners: Dr. Wendelin Werner

VVZ CR 3.2

Last Updated: 2026-02-05 15:55:00

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: BSC , DR , 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	Wed 08:15-10:00 (HG E 5) Thu 10:15-12:00 (ETF C 1)	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 (¬)
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 15 of the required 28 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 18 ECTS in the Theory and 12 ECTS in the Biology category. Note that some of the lectures are being recorded: )
  - Theory (At least 18 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.)
- Master Studies (Programme Regulations 2020)
  - Subject Specific Electives
- Master Studies (Programme Regulations 2014)
  - Specialization Areas and Electives
    - Statistical and Mathematical Courses
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 Courses
  - Mathematical Methods for Finance
Doctoral Department of Mathematics (More Information at: The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM. WARNING: Do not mistake ECTS credits for credit points for doctoral studies!)
- Graduate School (Official website of the Zurich Graduate School in Mathematics:)