On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations

Nathan E. Glatt-Holtz; Jonathan C. Mattingly; Geordie Richards

doi:10.1007/s10955-016-1605-x

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arXiv · 1512.04126

On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations

Nathan E. Glatt-Holtz·Jonathan C. Mattingly·Geordie Richards

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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.

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Nathan E. Glatt-Holtz, Jonathan C. Mattingly, Geordie Richards. 2015-12-13. On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations. https://doi.org/10.1007/s10955-016-1605-x

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