401-3642-00L  Brownian Motion and Stochastic Calculus

SemesterFrühjahrssemester 2022
DozierendeM. Schweizer
Periodizitätjährlich wiederkehrende Veranstaltung

KurzbeschreibungThis course gives an introduction to Brownian motion and stochastic calculus. It includes the construction and properties of Brownian motion, basics of Markov processes in continuous time and of Levy processes, and stochastic calculus for continuous semimartingales.
LernzielThis course gives an introduction to Brownian motion and stochastic calculus. The following topics are planned:
- Definition and construction of Brownian motion
- Some important properties of Brownian motion
- Basics of Markov processes in continuous time
- Stochastic calculus, including stochastic integration for continuous semimartingales, Ito's formula, Girsanov's theorem, stochastic differential equations and connections with partial differential equations
- Basics of Levy processes
SkriptLecture notes will be made available in class.
Literatur- R.F. Bass, Stochastic Processes, Cambidge University Press (2001).
- I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991).
- J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016).
- 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).
Voraussetzungen / BesonderesFamiliarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in
- J. Jacod, P. Protter, Probability Essentials, Springer (2004).
- R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010).