On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Glatt-Holtz, N; Mattingly, JC; Richards, G

Published Date

  • February 1, 2017

Published In

Volume / Issue

  • 166 / 3-4

Start / End Page

  • 618 - 649

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-016-1605-x

Citation Source

  • Scopus