Invariant measure selection by noise: An Example

Jonathan C. Mattingly , Etienne Pardoux (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: stochastic dynamically systems, Inviscid limits, zero--noise limit, invariant measure selection, stochastic dynamically systems.

Domaines: Mathématiques [math]; Probabilités [math.PR]

Jonathan C. Mattingly, Etienne Pardoux. Invariant measure selection by noise: An Example. Discrete and Continuous Dynamical Systems - Series A, 2014, 34 (10), pp.4223-4257. ⟨10.3934/dcds.2014.34.4223⟩. ⟨hal-01231866⟩