Probability and Stochastic Analysis - University of Bonn
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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 eberleadf@uni-bonnfdsa.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