On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
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© 2016 Springer Science+Business Media New YorkWe 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.
Published Version (Please cite this version)10.1007/s10955-016-1605-x
Publication InfoGlatt-Holtz, N; Mattingly, Jonathan Christopher; & Richards, G (2016). On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations. Journal of Statistical Physics. pp. 1-32. 10.1007/s10955-016-1605-x. Retrieved from http://hdl.handle.net/10161/11277.
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James B. Duke Professor
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and