带有加性噪声的随机热方程的概率一命中率

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-06-06 DOI:10.1007/s10959-024-01342-4

Robert C. Dalang, Fei Pu

引用次数: 0

摘要

我们研究了在迪里夏特边界条件下，d 随机热方程组的解的命中概率。我们证明，对于任何具有正（(d-6)\）维容量的有界伯乐集合，解几乎肯定会访问这个集合。

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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Hitting with Probability One for Stochastic Heat Equations with Additive Noise

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive \((d-6)\)-dimensional capacity, the solution visits this set almost surely.

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.