Empiric stochastic stability of physical and pseudo-physical measures

Understand

We define the empiric stochastic stability of an invariant measure in the finite-time scenario, the classical definition of stochastic stability.

• We prove that an invariant measure of a continuous system is empirically stochastically stable if and only if it is physical.
• We also define the empiric stochastic stability of a weak*-compact set of invariant measures instead of a single measure.
• Even when the system has not physical measures it still has minimal empirically stochastically stable sets of measures.