On Unique Ergodicity in Nonlinear Stochastic Partial Differential Equations
Date
2016-08-31
Authors
Journal Title
Journal ISSN
Volume Title
Repository Usage Stats
views
downloads
Citation Stats
Abstract
© 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.
Type
Department
Description
Provenance
Subjects
Citation
Permalink
Published Version (Please cite this version)
Publication Info
Glatt-Holtz, N, G Richards and JC Mattingly (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 https://hdl.handle.net/10161/11277.
This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.
Collections
Scholars@Duke
![Mattingly](https://scholars.duke.edu/profile-images/thumbnail200/0297691.jpg)
Jonathan Christopher Mattingly
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 Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.
His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.
Since 2013 he has also been working to understand and quantify gerrymandering and its interaction of a region's geopolitical landscape. This has lead him to testify in a number of court cases including in North Carolina, which led to the NC congressional and both NC legislative maps being deemed unconstitutional and replaced for the 2020 elections.
He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS and the AMS. He was awarded the Defender of Freedom award by Common Cause for his work on Quantifying Gerrymandering.
Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.