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<p>We investigate the distribution and clustering of extreme events of stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5385_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. We do so by studying the action of an annealed transfer operators on suitable spaces of densities. The spectral properties of such operators are obtained by employing a mixture of techniques coming from SDE theory and a functional analytic approach to dynamical systems.</p>

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Extreme Value Theory and Poisson Statistics for Discrete Time Samplings of Stochastic Differential Equations

  • 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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  • F. Flandoli,
  • S. Galatolo,
  • P. Giulietti,
  • S. Vaienti

摘要

We investigate the distribution and clustering of extreme events of stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on \({\mathbb {R}}^n\) R n . We do so by studying the action of an annealed transfer operators on suitable spaces of densities. The spectral properties of such operators are obtained by employing a mixture of techniques coming from SDE theory and a functional analytic approach to dynamical systems.