自相似马氏过程的Hausdorff维数(英文)

Hausdorff Dimension Results of Processes with Self-Similar Components

本文讨论了取值于 Rd的随机过程 Xt=( X1 ( t) ,X2 ( t) ,… ,XN( t) ) ,并且在一定条件下获得了 Xt的像集和图集的 Hausdorff维数 .这里 Xi( t) ,t∈ R+是独立的取值于 Rdi 的αi-自相似马氏过程 ,并且 ∑Ni=1 di=d.

In this paper, processes of the form X(t)=(X 1(t),X 2(t),…,X N(t)) where X i(t)(t∈R +) is an independent α i self similar Markov process in R d i and d=∑ N i=1 d i, are considered. The Hausdorff dimensions of the image and graph set of X(t) are obtained under certain mild conditions.