**Graduate Seminar on Stochastic Analysis (S4F3)**

# Reversible Diffusion Processes SoSem 2012

**Andreas Eberle**

**Time:** Wednesdays 10-12

*There are still a few talks available – if you are interested please send an E-Mail to eberle@uni-bonn.de .*

**Prerequisites: **Basics of Stochastic Analysis.

**Contents: **The seminar covers different topics related to reversible diffusion processes. During the first talks, we give an introduction to fundamental tools including Dirichlet forms, spectral theory, functional inequalities and potential theory. Afterwards, several recent research topics where these techniques are useful will be studied. Possible topics include:

**Mc Kean-Vlasov equations and propagation of chaos:**Mc Kean-Vlasov equations are nonlinear SDE with coefficients depending on the law of the process. They arise when studying mean-field interacting particle systems.

**Langevin and inertial Langevin equations.****Diffusion approximations for Metropolis algorithms.****Brownian motion on Riemannian manifolds.**

**References:**

Basics:

Ma/Röckner: Dirichlet forms

Fukushima/Oshima/Takeda: Dirichlet forms and symmetric Markov Processes

Royer: An initiation to logarithmic Sobolev inequalities

Villani: Optimal Transport- Old and new

Advanced Topics:

Sznitman: Lectures on Propagation of Chaos, Ecole d'été St. Flour

Hsu: Stochastic analysis on manifolds

Various research papers on different topics