Duke Applied Mathematics

Publications [#300245] of Jonathan C. Mattingly

Papers Published

1. Glatt-Holtz, N; Richards, G; Mattingly, JC, On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations, vol. 166 no. 3-4 (2015), pp. 618-649, Springer Nature [1512.04126v1], [doi]
   (last updated on 2026/01/20)

   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.