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<p>We consider Lipschitz and Hölder continuous random dynamical systems defined by a distribution with a finite logarithmic moment. We prove that under suitable non-degeneracy conditions every stationary measure must be <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5425_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\log \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>log</mo> </math></EquationSource> </InlineEquation>-Hölder continuous.</p>

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Log-Hölder Regularity of Stationary Measures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月1日

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  • Grigorii Monakov

摘要

We consider Lipschitz and Hölder continuous random dynamical systems defined by a distribution with a finite logarithmic moment. We prove that under suitable non-degeneracy conditions every stationary measure must be \(\log \) log -Hölder continuous.