应用概率统计2024,Vol.40Issue(1) :139-156.DOI:10.3969/j.issn.1001-4268.2024.01.009

一类由空间粗糙高斯噪声驱动分数阶动力学方程的性质研究

Some Properties of Fractional Kinetic Equation with Gaussian Noise Rough in Space

陆伟东 刘俊峰
应用概率统计2024,Vol.40Issue(1) :139-156.DOI:10.3969/j.issn.1001-4268.2024.01.009

一类由空间粗糙高斯噪声驱动分数阶动力学方程的性质研究

Some Properties of Fractional Kinetic Equation with Gaussian Noise Rough in Space

陆伟东 1刘俊峰1
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作者信息

  • 1. 南京审计大学数学学院,南京,211815
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摘要

本文主要研究了一类空间粗糙高斯噪声驱动的分数阶动力学方程,其中高斯噪声关于时间是白色的,关于空间的相依结构由Hurst指数小于1/2的分数布朗运动的协方差刻画.基于Malliavin分析技巧,我们证明了该类方程温和解在Skorohod意义下的存在性.同时证明了其温和解矩的上、下界的估计.最后证明了其温和解关于时间和空间变量的Hölder连续性.

Abstract

In this article,we study a class of fractional kinetic equation driven by Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst index H<1/2 in space.By using the techniques of Malliavin calculus,we prove the existence of the solution in the Skorohod sense and establish the upper and lower bounds for the moments of the solution.We also deduce the Hölder continuity of the solution with respect to the time and space variables.

关键词

分数阶动力学方程/高斯噪声/Malliavin分析/矩估计/Hölder连续性

Key words

fractional kinetic equation/Gaussian noise/Malliavin calculus/moment bounds/Hölder continuity

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出版年

2024
应用概率统计
中国数学会概率统计学会

应用概率统计

CSTPCDCSCD北大核心
影响因子:0.263
ISSN:1001-4268
参考文献量36
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