随机微分方程离散时间抽样的极值理论和泊松统计

IF 2.6 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-09-01 DOI:10.1007/s00220-025-05385-4

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

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引用次数: 0

摘要

本文研究了在\({\mathbb {R}}^n\)上对随机微分方程的解进行抽样构造的随机过程的极端事件的分布和聚类。我们通过研究退火传递算符在合适密度空间上的作用来做到这一点。这些算符的谱性质是通过采用来自SDE理论和动力系统泛函分析方法的混合技术获得的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

We investigate the distribution and clustering of extreme events of stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on \({\mathbb {R}}^n\). 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.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.