FEYNMAN-KAC FORMULA FOR THE HEAT EQUATION DRIVEN BY FRACTIONAL NOISE WITH HURST PARAMETER H < 1/2

被引：33

作者：

Hu, Yaozhong ^{[1
]}

Lu, Fei ^{[1
]}

Nualarti, David ^{[1
]}

机构：

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

ANNALS OF PROBABILITY | 2012年 / 40卷 / 03期

基金：

美国国家科学基金会;

关键词：

Feynman-Kac integral; Feynman-Kac formula; stochastic partial differential equations; fractional Brownian field; nonlinear stochastic integral; fractional calculus; STOCHASTIC CALCULUS; INTEGRATION;

D O I：

10.1214/11-AOP649

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 paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter H < 1/2. To establish such a formula, we introduce and study a nonlinear stochastic integral from the given Gaussian noise. To show the Feynman-Kac integral exists, one still needs to show the exponential integrability of nonlinear stochastic integral. Then, the approach of approximation with techniques from Malliavin calculus is used to show that the Feynman-Kac integral is the weak solution to the stochastic partial differential equation.

引用

页码：1041 / 1068

页数：28

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FEYNMAN-KAC FORMULA FOR THE HEAT EQUATION DRIVEN BY FRACTIONAL NOISE WITH HURST PARAMETER H &lt; 1/2

FEYNMAN-KAC FORMULA FOR THE HEAT EQUATION DRIVEN BY FRACTIONAL NOISE WITH HURST PARAMETER H < 1/2