分式Brown运动代数和的一些性质

ON THE ALGEBRIC SUM OF FRACTIONAL BROWNIAN MOTIONS

在本文中我们研究 d 维分式 Brown 运动代数和的象集的性质.证明了:若 dimE>(ad)/m,则 X(E)(?)…(?)X(E)(m 项)a.s 具有内点.若 dimE>ad/2,dimF>ad/2则 X(E)-X(F)a.s.具有内点.这些结果推进了 Kahane,Mountford 和 Testard 关于Brown 运动及分式 Brown 运动的研究工作.

In this paper,we study properties of the images of algebric sum of d-di-mensional fractional Brownian motions.We prove that if E(?)R^N,dimE>(αd)/m,then X(E)(?)…(?)(E)(m times)a.s.has an interior point.If dimE(αd)/2.dimF>(ad)/2,then X(E)-X(F)a.s.han an interior point.These re-sults extend the results of Kahane,Mountford and Testard.