Extremes of the stochastic heat equation with additive Levy noise

被引：4

作者：

Chong, Carsten ^{[1
]}

Kevei, Peter ^{[2
]}

机构：

[1] Columbia Univ, New York, NY 10027 USA

[2] Univ Szeged, Szeged, Hungary

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2022年 / 27卷

关键词：

almost-sure asymptotics; integral test; Poisson noise; regular variation; stable noise; stochastic PDE; CONVOLUTION EQUIVALENCE; DRIVEN; INTERMITTENCY; DISTRIBUTIONS;

D O I：

10.1214/22-EJP855

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 analyze the spatial asymptotic properties of the solution to the stochastic heat equation driven by an additive Levy space-time white noise. For fixed time t > 0 and space x is an element of R-d we determine the exact tail behavior of the solution both for light-tailed and for heavy-tailed Levy jump measures. Based on these asymptotics we determine for any fixed time t > 0 the almost-sure growth rate of the solution as vertical bar x vertical bar -> infinity.

引用

页数：21

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Chong, Carsten ;

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Chong, Carsten ;

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ANNALS OF PROBABILITY, 2019, 47 (04) :1911-1948

[10] Path properties of the solution to the stochastic heat equation with Levy noise [J].

Chong, Carsten ;

Dalang, Robert C. ;

Humeau, Thomas .

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2019, 7 (01) :123-168

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