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<p>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.</p>

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Lipschitz regularity of the invariant measure of random dynamical systems

  • 期刊论文

  • 发表日期：

    2025年4月21日

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  • Davi Lima,
  • Rafael Lucena

摘要

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.