A NOTE ON A FENYMAN-KAC-TYPE FORMULA

被引：3
|
作者：
Balan, Raluca [1 ]
机构：
[1] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada
来源：
ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2009年 / 14卷
关键词：
fractional Brownian motion; stochastic heat equation; Feynman-Kac formula; planar Poisson process; EQUATIONS; NOISE;
D O I：
10.1214/ECP.v14-1468
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：
In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation in [0,1] x R(d), with multiplicative noise, which is fractional in time and colored in space. This representation is similar to the one given in [8] in the case of an s.p.d.e. driven by a Gaussian noise, which is white in time. Unlike the formula of [8], which is based on the usual Poisson process, our representation is based on the planar Poisson process, due to the fractional component of the noise.
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页码：252 / 260
页数：9
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