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19208001 Stochastische Analysis

Winter Term 2019/2020

lecture and exercise by Prof. Dr. Nicolas Perkowski


Time and place

  •  Lecture: Tuesdays, 08-10h, in seminar room 049, Takustr. 9, and 
                    Wednesdays, 08-10h, in seminar room 031, Arminallee 6.

  • Exercise Session: Wednesdays, 14-16h, in room 025/026, Arnimallee 6.
  • Final Exam:  to be announced in due course

Assessment

To receive credits fo the course you need to

  • actively participate in the exercise session 
  • work on and successfully solve the weekly exercises 
  • pass the final exam (see above)

If you are an FU student you only need to register for the course via CM (Campus Management).
    

Exercises 

Problem sets will be put online every Wednesday and can be found under Assignements in the KVV/Whiteboard portal. Solutions (in pairs!) are due by 4pm on Wednesday of the following week  –  please submit either using the mailbox A8 on the ground floor in Arnimallee 3-5 or in the exercise session.

Requirements: Prerequisites are Analysis I-III and Stochastics I and II. Functional analysis is helpful but not required.

Course Overview/ Content:

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:
Gaussian processes; Brownian motion, construction and properties; filtrations and stopping times; continuous time martingales; continuous semimartingales; quadratic variation; stochastic integration; Itô’s formula; Girsanov’s theorem and change of measure; time change; martingale representation; stochastic differential equations and diffusion processes, connections with partial differential equations.

References

  • Jean-François Le Gall: Brownian motion, martingales, and stochastic calculus. Springer, 2016.
  • Ioannis Karatzas and Steven E. Shreve: Brownian motion and stochastic calculus. Springer, 1988.
  • Daniel Revuz and Marc Yor: Continuous martingales and Brownian motion. Springer, 3rd edition, 1999.
  • Achim Klenke: Probability Theory - A Comprehensive Course. Springer, 2008.
  • Peter Mörters and Yuval Peres: Brownian motion. Cambridge University Press, 2010.
  • There will also be lecture notes with additional references.