Student Probability Seminar

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Unique ergodicity, ellipticity, and Feller properties

Speaker: Eric Thoma, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, March 2, 2020, 11:45 a.m.

Synopsis:

I will give an introduction to ergodicity for Markov semigroups, and, through concrete examples, show various conditions that imply unique ergodicity in action. These conditions have a lot to do with notions of "ellipticity" (e.g. Hörmander's condition). Time permitting, I will explain the general approach of Hairer and Mattingly's 2006 Annals paper, which proved unique ergodicity of the 2D stochastic Navier-Stokes equation. The only assumed background will be some familiarity with stochastic calculus, probability, and differential equations.