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Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - RTG1845

Humboldt-Universität zu Berlin | Faculty of Mathematics and Natural Sciences | Department of Mathematics | RTG1845 | Qualification program | Minicourses | Kulik | "Coupling method with applications to ergodicity, limit theorems, and spectral properties of Markov processes"

"Coupling method with applications to ergodicity, limit theorems, and spectral properties of Markov processes"

 

Lecture 1: Doeblin theorem on uniform geometrical ergodicity; Harris theorem (i.e the extension of the Doeblin theorem with the recurrence rate controlled via a Lyapunov type condition); Dobrushin lemma and the above theorems with the minorization condition replaced by the Dobrushin type irreducibility condition; generalized Harris theorem for a metric weaker than the total variation metric (by Hairer, Mattungly and Scheutzow).

 

Lecture 2: LLN and CLT for stationary Markov processes. Coupling approach for proving LLN and CLT for non-stationary Markov processes. Averaging and diffusion approximation.

 

Lecture 3. Versions of the Lyapunov condition. Spectral gap I: time-reversible processes. Spectral gap II: time-irreversible processes, interpolation theorems approach.