Small ball probability estimates for the Holder semi-norm of the stochastic heat equation

被引：5

作者：

Foondun, Mohammud ^{[1
]}

Joseph, Mathew ^{[2
]}

Kim, Kunwoo ^{[3
,4
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, 26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

[2] Indian Stat Inst, Stat Math Unit, 8th Mile Mysore Rd, Bangalore 560059, Karnataka, India

[3] Pohang Univ Sci & Technol POSTECH, Pohang 37673, Gyeongbuk, South Korea

[4] Korea Inst Adv Study KIAS, Sch Math, Seoul 02455, South Korea

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2023年 / 185卷 / 1-2期

基金：

新加坡国家研究基金会;

关键词：

Heat equation; White noise; Stochastic partial differential equations; Small ball; SUPPORT THEOREM;

D O I：

10.1007/s00440-022-01153-w

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the stochastic heat equation on [0, 1] with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Holder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Holder semi-norms.

引用

页码：553 / 613

页数：61

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