分数布朗单驱动的一类随机偏微分方程的弱解
Weak Solution for Stochastic Partial Differential Equations Driven by a Fractional Brownian Sheet withMonotone Drift
DOI: 10.12677/AAM.2019.811206, PDF, 下载: 743  浏览: 2,652 
作者: 夏晓宇, 闫理坦：东华大学理学院，上海
关键词: 分数布朗单；随机偏微分方程；弱解；Fractional Brownian Sheet； Stochastic Partial Differential Equation； Weak Solution
摘要:

本文旨在研究分数布朗单驱动的一类随机偏微分方程的弱解问题。首先，BH,H′={BH,H′，z∈[0，T]2}为一个分数布朗单，其中Hurst指数为(H,H′),我们考虑随机偏微分方程

并限定系数b ，使它满足所谓的局部线性增长条件。随后证明了这类随机偏微分方程弱解的存在唯一性。

In this note,we will study weak solution of hyperbolic stochastic partial differential Equation (1). Where BH,H′={BH,H′，z∈[0，T]2} is a Fractional Brownian sheet and b is under the so-called locally linear growth condition.

Then we prove the existence and uniqueness of the weak solution of this kind of stochastic difffferential equation.

文章引用：夏晓宇, 闫理坦. 分数布朗单驱动的一类随机偏微分方程的弱解[J]. 应用数学进展, 2019, 8(11): 1766-1774. https://doi.org/10.12677/AAM.2019.811206

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