Stochastic Analysis, Summer Semester 2016

Information for the lecture Stochastic Analysis by Prof. Dr. Nicolas Perkowski and Dr. Achref Bachouch (SoSe 2016): Information sheet.

This is a BMS course that will be taught in English to facilitate participation of international students.


Gaussian processes; white noise; Brownian motion and its path properties; filtrations and stopping times;

continuous time martingales; continuous semimartingales; quadratic variation; stochastic integration;
Itô’s formula; Burkholder’s inequality; change of measure; martingale representation; stochastic differential
equations: existence and uniqueness, Markov property, link with partial differential equations.


Analysis I and II, Stochastics I and II. Recommended: Analysis III and basic knowledge of Functional Analysis.

Current information:

- An updated version of the lecture notes is available: Lecture notes (Without proofs. Version of 01-08-2016) .

- Solution for Sheet 13 is available: Solution .

- Solution for Sheet 10, exercise 10.2 is available: Solution .

- Solution for Sheet 9, exercise 9.2 is available: Solution .

- Solution for Sheet 8, questions 8.1.b and 8.1.c is available: Solution .

- A new reference has been added: Lecture notes of P. Priouret .

Lecture (N. Perkowski and A.Bachouch)
  • Monday, 13-15 in room 1'013, RUD 25
  • Wednesday, 13-15 in room 0311, RUD 26

Exercise session (A.Bachouch)
  • Monday, 15-17 in room 3'008, RUD 25

  • You may submit your solutions in groups of two.

  • Grader: Mr. Florian Stelzer. 
           -  Email:
           If you have questions concerning your marked submissions, please send an email to Mr. Stelzer.
  • Every week, solutions will be presented by students.

Lecture notes (without proofs. Version of 01-08-2016).

Exercise Sheets


       - J.F. Le Gall lecture notes

       - P. Priouret lecture notes
       - J. Jacod lecture notes
       - I. Karatzas and S. Shreve. Brownian motion and stochastic calculus. 2nd ed. Graduate Texts in Mathematics, 113. New York etc.: Springer-Verlag (1991)
       - D. Revuz and M. Yor. Continuous martingales and Brownian motion. 3rd ed. Graduate Texts in Mathematics, 293. Berlin: Springer (1999)

       - P. Mörters and Y. Peres. Brownian Motion. 1st ed. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press (2010)

       - G. Lowther’s blog:

       - Functional analysis material:

                         - Lecture notes by G. Teschl

                         - Extremely short overview by A. Wibisino

Office hours: by agreement.


Name E-mail Office
Prof. Dr. Nicolas Perkowski
RUD 25, 1.201
Dr. Achref Bachouch   RUD 25, 1.227