The stochastic wave equation driven by fractional Brownian noise and temporally correlated smooth noise

被引：22

作者：

Caithamer, P ^{[1
]}

机构：

[1] Univ So Indiana, Dept Math, Evansville, IN 47712 USA

来源：

STOCHASTICS AND DYNAMICS | 2005年 / 5卷 / 01期

关键词：

stochastic partial differential equation; fractional Brownian motion; energy; deviations;

D O I：

10.1142/S0219493705001286

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：

The stochastic wave equation in one spatial dimension driven by a class of fractional noises or, alternately, by a class of smooth noises with arbitrary temporal covariance is studied. In either case, the wave equation is explicitly solved and the upper and lower bounds on both the large and small deviations of several sup norms associated with the solution are given. Finally the energy of a system governed by such an equation is calculated and its expected value is found.

引用

页码：45 / 64

页数：20

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