分数布朗单驱动的一类随机偏微分方程的弱解

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.