Invariant measure selection by noise: An Example
Probability
2014-03-17 v1 Dynamical Systems
Fluid Dynamics
Abstract
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.
Cite
@article{arxiv.1403.3593,
title = {Invariant measure selection by noise: An Example},
author = {Jonathan C. Mattingly and Etienne Pardoux},
journal= {arXiv preprint arXiv:1403.3593},
year = {2014}
}