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.
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页码：4681 / 4703
页数：23
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