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arXiv · 1707.01472

Empiric stochastic stability of physical and pseudo-physical measures

Eleonora Catsigeras
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Abstract

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. We prove that such sets are necessarily composed by pseudo-physical measures. Finally, we apply the results to the one-dimensional C1-expanding case to conclude that the measures of empirically stochastically sets satisfy Pesin Entropy Formula.

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Eleonora Catsigeras. 2017-07-05. Empiric stochastic stability of physical and pseudo-physical measures. https://arxiv.org/abs/1707.01472

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