Objectives:
This course provides an introduction into the theory of discrete time stochastic processes. We cover martingales in discrete time (existence, convergence results, ...), Markov Chains, construction of general discrete time processes, construction of Brownian motion and many other topics.
Lecture:
- Mo. 13:15 - 14:45; Room 0'311 (RUD26)
- Thu. 9:15 - 10:45; Room 1.304 (RUD26)
Tutorial:
- Tue. 13:15 - 14:45; Room 1'304 (RUD26)
Content:
- Conditional expectations
- Martingales in discrete time
- Markov chains: recurrence, transience, invariant measures
- Construction of stochastic processes
- Brownian motion, weak convergence on metric spaces, Donsker's invariance principle
Literature: (my personal favorites are the books by Bauer)
- Heinz Bauer: Wahrscheinlichkeitstheorie (De Gruyter. 2002)
- Heinz Bauer: Maß- und Integrationstheorie (De Gruyter, 1992)
- Jean Jacod & Philip E. Protter: Probability Essentials (Springer, 2004)
- Achim Klenke: Wahrscheinlichkeitstheorie / Probability Theory (Springer, 2013)
- David Williams: Probability with Martingales (Cambridge, University Press, 1991)
- Richard Durrett: Probability: Theory and Examples (Duxbury Press, 1996)
- A.N. Shiryaev: Wahrscheinlichkeit / Probability-1 (Dt. Verlag der Wissenschaft, 1988 / Springer, 2016)
- Patrick Billingsley: Convergence of Probability Measures (Wiley, 1999)
Lecture Notes: tba
First lecture: Thursday, Oct. 17. First exercise: Tuesday, Oct. 29. The course will be given in English upon request.