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

共 22 条

[11]

Fournier N, 2002, MATH COMPUT, V71, P583, DOI 10.1090/S0025-5718-01-01339-4

[12]

HERSCH R, 1974, ROCKY MT J MATH, V4, P443

[13]

Kac M., 1956, LECT PURE APPL SCI, V2, P497

[14]

Kac M, 1974, ROCKY MOUNTAIN J MAT, V4, P497, DOI [10.1216/RMJ-1974-4-3-497, DOI 10.1216/RMJ-1974-4-3-497]

[15]

Karatzas I., 1998, Brownian Motion and Stochastic Calculus, Vsecond

[16]

LEVEQUE O, 2001, THESIS ECOLE POLYTEC

[17]

Mueller C, 1997, ANN PROBAB, V25, P133

[18] Asymptotic properties of the solutions to stochastic KPP equations [J].

Oksendal, B ;

Våge, G ;

Zhao, HZ .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2000, 130 :1363-1381

[19]

Schwartz L., 1966, Theorie des Distributions

[20]

WALSH JB, 1986, LECT NOTES MATH, V1180, P265

← 1 2 3 →