Stochastic Analysis (HS 2022)

Lectures: Monday 10:15-12:00 and Tuesday 8:15-10:00.

Exercises: Thursday 8:15-10:00, assistant Ramon Locher

Summary: The course gives an introduction to the theory of stochastic processes in continuous time. The following topics will be discussed:

• Brownian motion
• Martingales in continuous time
• Markov processes
• Stochastic calculus
• Levy processes
• Stochastic differential equations

Lectures content will be provided in form of handwritten notes from the lectures and pointers to the literature on ADAM.

Questions for exercises are disponible on ADAM.

Literature:

• J.-F. Le Gall: Brownian Motion, Martingales, and Stochastic Calculus
• D. Revuz, M. Yor: Continuous martingales and Brownian motion
• I. Karatzas, S. Shreve: Brownian motion and stochastic calculus
• L.C.G. Rogers, D. Williams: Diffusions, Markov processes and martingales, 1 and 2
• D.W. Stroock, S.R.S. Varadhan: Multidimensional diffusion processes
• R. Durrett: Stochastic calculus: A practical introduction