401-3642-00L  Brownian Motion and Stochastic Calculus

Semester Spring Semester 2012
Lecturers M. Schweizer
Periodicity yearly course
Language of instruction English


Abstract This is a first course on continuous-time stochastic processes. It covers basic notions of stochastic calculus. The following topics will be discussed:
- Brownian motion
- Markov processes
- Stochastic calculus
- Levy processes
Objective This is a first course on continuous-time stochastic processes. It covers basic notions of stochastic calculus. The following topics will be discussed:
- Brownian motion: definition, construction, some important properties
- Markov processes: basics, strong Markov property, generators and martingale problems
- Stochastic calculus: semimartingales, stochastic integrals, Ito formula, Girsanov transformation, stochastic differential equations
- Levy processes: basic notions, some important properties
Content This is a first course on continuous-time stochastic processes. It covers basic notions of stochastic calculus. The following topics will be discussed:
- Brownian motion: definition, construction, some important properties
- Markov processes: basics, strong Markov property, generators and martingale problems
- Stochastic calculus: semimartingales, stochastic integrals, Ito formula, Girsanov transformation, stochastic differential equations
- Levy processes: basic notions, some important properties
Lecture notes will be available for purchase
Literature Durrett, R., "Stochastic Calculus. A Practical Introduction", CRC Press, 1996.
Ikeda, N. and Watanabe, S., "Stochastic Differential Equations and Diffusion Processes", second edition, North Holland, Amsterdam, 1979.
Karatzas, I. and Shreve, S., "Brownian Motion and Stochastic Calculus", second edition, Springer, Berlin, 1991.
Revuz, D. and Yor, M., "Continuous Martingales and Brownian Motion", second edition, Springer, Berlin, 1994.
Rogers, L.C.G. and Williams, D., "Diffusions, Markov Processes, and Martingales", vol. 1 and 2, Wiley, Chichester, 2000, 1994.
Sato, K., "Levy Processes and Infinitely Divisible Distributions", Cambridge University Press, 1999.
Prerequisites / Notice This course replaces the former course 401-3642-00L Stochastic Processes and Stochastic Analysis. Moreover it has a large overlap with the course 401-4608-10L Brownian Motion and Stochastic Calculus from FS 2010. Therefore it is forbidden to register for an examination for more than one of the three courses mentioned.