A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.'s

被引：28

作者：

Dalang, Robert C. ^{[1
]}

Mueller, Carl ^{[2
]}

Tribe, Roger ^{[3
]}

机构：

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

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

[3] Univ Warwick, Dept Math, Coventry CV4 7AL, W Midlands, England

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 360卷 / 09期

关键词：

D O I：

10.1090/S0002-9947-08-04351-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish a probabilistic representation for a wide class of linear deterministic p.d.e.'s with potential term, including the wave equation in spatial dimensions 1 to 3. Our representation applies to the heat equation, where it is related to the classical Feynman-Kac formula, as well as to the telegraph and beam equations. If the potential is a (random) spatially homogeneous Gaussian noise, then this formula leads to an expression for the moments of the solution.

引用

页码：4681 / 4703

页数：23

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