Introduction to invariant measure and Unique ergodicity for SPDEs
Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations August 24, 2015 - August 28, 2015
Location: MSRI: Simons Auditorium
Markov transition kernel
invariant ergodic measure
basic existence and uniqueness theorems
58J51 - Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
28Dxx - Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]
28C10 - Set functions and measures on topological groups or semigroups, Haar measures, invariant measures [See also 22Axx, 43A05]
I will begin by discussing invariant measures for finite dimensional Markov Processes. I will consider some classical conditions for existence and uniqueness in the finite dimensional setting. Then I will show how the situation becomes more complicated in the infinite dimensional setting of and SPDE. I will mainly concentrate on dissipative SDPEs. Time permitting I will discuss Malliavin calculus and some ideas of Hypo-ellipticity in infinite dimensions
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