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## Stochastic Analysis (HS 2020)

**Lectures:** Monday and Tuesday 10:15-12:00, online via Zoom, link in ADAM

**Exercises:** Thursday 8:15-10:00, online via Zoom (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. Video recordings will be made
available on demand.

**Questions for exercises:** will appear here or on ADAM.

- TBD

**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