分数噪声驱动的随机热方程解的局部时

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 582-595.

分数噪声驱动的随机热方程解的局部时

王志¹(),闫理坦²(),余显烨^3,*()

¹ 宁波工程学院理学院浙江宁波 315211
² 东华大学理学院上海 201620
³ 中山大学数学学院广州 510275

收稿日期:2017-11-02 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 余显烨 E-mail:wangzhi1006@hotmail.com;litanyan@hotmail.com;xianyeyu@gmail.com
作者简介:王志, wangzhi1006@hotmail.com|闫理坦, litanyan@hotmail.com
基金资助:
国家自然科学基金(11701304);国家自然科学基金(11571071);国家自然科学基金(11701589);浙江省自然科学基金(LQ16A010006);中央高校基本科研业务费(171gpy17)

Local Times of the Solution to Stochastic Heat Equation with Fractional Noise

Zhi Wang¹(),Litan Yan²(),Xianye Yu^3,*()

¹ School of Sciences, Ningbo University of Technology, Zhejiang Ningbo 315211
² Department of Mathematics, College of Science, Donghua University, Shanghai 201620
³ School of Mathematics, Sun Yat-sen University, Guangzhou 510275

Received:2017-11-02 Online:2019-06-26 Published:2019-06-27
Contact: Xianye Yu E-mail:wangzhi1006@hotmail.com;litanyan@hotmail.com;xianyeyu@gmail.com
Supported by:
the NSFC(11701304);the NSFC(11571071);the NSFC(11701589);the Zhejiang Provincial Natural Science Foundation(LQ16A010006);the Fundamental Research Funds for the Central Universities(171gpy17)

摘要/Abstract

摘要：

该文研究了可加分数噪声驱动的随机热方程解的碰撞局部时和相交局部时.运用局部非确定性和混沌分解等方法得到它们的存在性和光滑性.

关键词: 随机热方程, 分数噪声, 碰撞局部时, 相交局部时, 混沌分解

Abstract:

In this paper, we study the collision and intersection local times of the solution to stochastic heat equation with additive fractional noise. We mainly prove its existence and smoothness properties through local nondeterminism and chaos expansion.

Key words: Stochastic heat equation, Fractional noise, Collision local time, Intersection local time, Chaos expansion

中图分类号:

O211.6

王志,闫理坦,余显烨. 分数噪声驱动的随机热方程解的局部时[J]. 数学物理学报, 2019, 39(3): 582-595.

Zhi Wang,Litan Yan,Xianye Yu. Local Times of the Solution to Stochastic Heat Equation with Fractional Noise[J]. Acta mathematica scientia,Series A, 2019, 39(3): 582-595.

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