Intermittency properties in a hyperbolic Anderson problem

被引：23

作者：

Dalang, Robert C. ^{[1
]}

Mueller, Carl ^{[2
]}

机构：

[1] Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland

[2] Univ Rochester, Dept Math, Rochester, NY 14627 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2009年 / 45卷 / 04期

关键词：

Stochastic wave equation; Stochastic partial differential equations; Moment Lyapunov exponents; Intermittency; Stochastic heat equation; STOCHASTIC WAVE-EQUATION; MODEL; DIMENSIONS;

D O I：

10.1214/08-AIHP199

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 study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous Gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations. For comparison, we also derive bounds on moments of the solution to the stochastic heat equation with the same linear multiplicative noise.

引用

页码：1150 / 1164

页数：15

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