Moment bounds and asymptotics for the stochastic wave equation

被引：8

作者：

Chen, Le ^{[1
]}

Dalang, Robert C. ^{[1
]}

机构：

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

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 04期

关键词：

Nonlinear stochastic wave equation; Hyperbolic Anderson model; Intermittency; Growth indices; SMOOTHNESS; EXISTENCE; VALUES;

D O I：

10.1016/j.spa.2014.11.009

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 wave equation on the real line driven by space time white noise and with irregular initial data. We give bounds on higher moments and, for the hyperbolic Anderson model, explicit formulas for second moments. These bounds imply weak intermittency and allow us to obtain sharp bounds on growth indices for certain classes of initial conditions with unbounded support. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：1605 / 1628

页数：24

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