On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
Probability
2016-09-21 v1 Analysis of PDEs
Abstract
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart possesses a finite number of determining modes. Examples exhibiting parabolic and hyperbolic structure are studied in detail. In the later situation we also present a simple framework for establishing the existence of invariant measures when the usual approach relying on the Krylov-Bogolyubov procedure and compactness fails.
Cite
@article{arxiv.1512.04126,
title = {On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations},
author = {Nathan E. Glatt-Holtz and Jonathan C. Mattingly and Geordie Richards},
journal= {arXiv preprint arXiv:1512.04126},
year = {2016}
}