On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
| Autor: | Geordie Richards, Jonathan C. Mattingly, Nathan Glatt-Holtz |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
010102 general mathematics
Ergodicity Probability (math.PR) Statistical and Nonlinear Physics 01 natural sciences 010101 applied mathematics Stochastic partial differential equation Nonlinear system Mathematics - Analysis of PDEs Compact space Hyperbolic set FOS: Mathematics Applied mathematics Uniqueness 0101 mathematics Invariant (mathematics) Finite set Mathematics - Probability Mathematical Physics Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1512.04126 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|