Publications [#243878] of Jonathan C. Mattingly
- Mattingly, JC; Pardoux, E, Invariant measure selection by noise. An example,
Discrete and Continuous Dynamical Systems Series A, vol. 34 no. 10
pp. 4223-4257, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947 [arXiv:1403.3593], [repository], [doi]
(last updated on 2020/07/12)
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.