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<p>We consider smooth random dynamical systems defined by a distribution with a finite moment of the norm of the differential, and prove that under suitable non-degeneracy conditions any stationary measure must be Hölder continuous. The result is a vast generalization of the classical statement on Hölder continuity of stationary measures of random walks on linear groups.</p>

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Hölder regularity of stationary measures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月19日

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  • Anton Gorodetski,
  • Victor Kleptsyn,
  • Grigorii Monakov

摘要

We consider smooth random dynamical systems defined by a distribution with a finite moment of the norm of the differential, and prove that under suitable non-degeneracy conditions any stationary measure must be Hölder continuous. The result is a vast generalization of the classical statement on Hölder continuity of stationary measures of random walks on linear groups.