Ergodicity of Markov Processes: A marriage of topology and measure theory
Ergodicity of Markov Processes: A marriage of topology and measure theory

Martin Hairer, Courant Institute for Mathematics, NYC
Sherrerd Hall 101
One very widely used criterion in the theory of Markov chains states that if a Markov operator has the strong Feller property and is topologically irreducible, then it can have at most one invariant measure. While this criterion is very useful in finitedimensional situations, it fails for many infinitedimensional problems. In this talk, we will present two different generalisations of the strong Feller property that can be applied to a much larger class of problems. These include semilinear parabolic stochastic PDEs, stochastic delay equations, and diffusions driven by fractional noise.