设{Ws,t}是一取值于Rd(d≥3)的布朗单,qd表B esse l函数Jd2-2(x)的第一正零点,b是任意正实数.令p0,q0>0,k0=m in{p0,q0},Δb=[p0,p0+b]×[q0,q0+b],用μΔWb.,.(B(x,ε))表{Ws,t}在指标区间Δb内,在中心为x,半径为ε的球B(x,τ)...设{Ws,t}是一取值于Rd(d≥3)的布朗单,qd表B esse l函数Jd2-2(x)的第一正零点,b是任意正实数.令p0,q0>0,k0=m in{p0,q0},Δb=[p0,p0+b]×[q0,q0+b],用μΔWb.,.(B(x,ε))表{Ws,t}在指标区间Δb内,在中心为x,半径为ε的球B(x,τ)里由直线上局部蔓延导致的占有测度.对任给a∈(0,4k0q2d),则使得lim supε→0μWΔ.,.b(B(Ws,t,ε))4ε(logε5)-1≥a的(s,t)∈Δb点的集合的H ausdorff维数a.s.大于等于2-k0aq2d4.展开更多
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.
