Lipschitz regularity of the invariant measure of random dynamical systems

Abstract

In this article we derive a regularity result for the disintegration of the invariant measure associated to a class of Random Dynamical Systems - RDS. The results of this work are obtained by constructing a suitable anisotropic normed space defined by the Wasserstein-Kantorovich-like metric and understanding the dynamics of the associated transfer operator in a neighborhood of its fixed point. Precisely, we employ functional analytic techniques to demonstrate a spectral gap for its action on suitable spaces of signed measures. We apply this analysis to prove an exponential decay of correlation statement for Lipschitz observables and statistical properties of the RDS.

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References in corpus (3)

• Spectral gap and quantitative statistical stability for systems with contracting fibers and Lorenz-like maps
• Hölder regularity and exponential decay of correlations for a class of piecewise partially hyperbolic maps
• Quantitative statistical stability for the equilibrium states of piecewise partially hyperbolic maps

Cited by in corpus (1)

• Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches