# American Institute of Mathematical Sciences

October  2014, 34(10): 4223-4257. doi: 10.3934/dcds.2014.34.4223

## Invariant measure selection by noise. An example

 1 Mathematics Department and Department of Statisical Science, Statisical Science Duke University, Box 90320, Durham, NC 27708-0320, United States 2 Laboratoire d'Analyse, Topologie, Probabilités, Université de Provence 39, rue F. Joliot-Curie, F-13453 Marseille cedex 13, France

Received  March 2013 Revised  October 2013 Published  April 2014

We consider a deterministic system with two conserved quantities and infinity many invariant measures. However the systems possess a unique invariant measure when enough stochastic forcing and balancing dissipation are added. We then show that as the forcing and dissipation are removed a unique limit of the deterministic system is selected. The exact structure of the limiting measure depends on the specifics of the stochastic forcing.
Citation: Jonathan C. Mattingly, Etienne Pardoux. Invariant measure selection by noise. An example. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4223-4257. doi: 10.3934/dcds.2014.34.4223
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##### References:
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