19208001 Stochastik III
- FU-Students only need to register via Campus Management, then they will be automatically registered also in MyCampus/Whiteboard.
- Non-FU-students are required to register via MyCampus/Whiteboard.
- The course material will be distributed via MyCampus/Whiteboard.
Winter Term 2020/2021
Time and place
Lecture: Mondays, 12--14h, online, and
Wednesdays, 10--12h, online.
- Exercise Session: Wednesdays, 12--14h, online.
- Final Exam: to be announced in due course
Requirements: Prerequisites are Analysis I-III and Stochastics I and II. Functional analysis is helpful but not required.
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)
Problem sets will be put online every Wednesday and can be found under Assignements in the MyCampus/Whiteboard portal. Solutions (in pairs!) are due on Wednesday of the following week – please submit either by uploading the solutions via Whiteboard or by handing them in via email.
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.
- 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.
- In the Whiteboard system there will also be lecture notes with additional references.