A Feynman-Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise

被引：5
作者：
Kim, Hyun-Jung [1 ]
Scorolli, Ramiro [2 ]
机构：
[1] UCSB Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
[2] Univ Bologna, Dipartimento Sci Stat Paolo Fortunati, Bologna, Italy
来源：
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2023年 / 26卷 / 03期
关键词：
Wick product; stochastic heat equation; space-only white noise; Wiener chaos; Feynman-Kac formula; multiple Wiener integral; Holder regularity; white noise analysis; Malliavin calculus; ANDERSON MODEL; DISTRIBUTIONS; CONSTRUCTION; SPACES;
D O I：
10.1142/S0219025723500017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the (unique) mild solution u(t, x) of a one-dimensional stochastic heat equation on [0, T] x R driven by time-homogeneous white noise in the Wick-Skorokhod sense. The main result of this paper is the computation of the spatial derivative of u(t, x), denoted by partial derivative(x)u(t, x), and its representation as a Feynman-Kac type closed form. The chaos expansion of partial derivative(x)u(t, x) makes it possible to find its (optimal) Holder regularity especially in space.
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页数：35
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