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...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.展开更多
基金Supported by the National Natural Science Foundation of China(11271020)the Distinguished Young Scholars Foundation of Anhui Province(1608085J06)+1 种基金the National Natural Science Foundation of China(11361007)the Natural Science Foundation of Universities of Anhui Province(KJ2014A180,KJ2016A527)
基金Supported by the National Natural Science Foundation of China(11271020)the Natural Science Foundation of Universities of Anhui Province(KJ2012Z284KJ2012Z286)
文摘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.
