Uniform dimension results of multi-parameter stable processes  

作　　者：林火南 

出　　处：《Science China Mathematics》1999年第9期932-944,共13页中国科学：数学（英文版）

基　　金：Project supported by Fujian Natural Science Foundation.

摘　　要：The problem of uniform dimensions for multi-parameter processes, which may not possess the uniform stochastic H?lder condition, is investigated. The problem of uniform dimension for multi-parameter stable processes is solved. That is, ifZ is a stable (N,d, α)-process and αN ?d, then $$\forall E \subseteq \mathbb{R}_ + ^N , \dim Z\left( E \right) = \alpha \cdot \dim E$$ holds with probability 1, whereZ(E) = {x : ?t ∈E,Z t =x} is the image set ofZ onE. The uniform upper bounds for multi-parameter processes with independent increments under general conditions are also given. Most conclusions about uniform dimension can be considered as special cases of our results.The problem of uniform dimensions for multi-parameter processes, which may not possess the uniform stochastic H(?)lder condition, is investigated. The problem of uniform dimension for multi-parameter stable processes is solved. That is, if Z is a stable (N, d, α)-process and αN≤d, then (?)E(?)R_+~N, dimZ(E)=α·dimE holds with probability 1, where Z(E)={x:(?)t∈E, Z_t=x} is the image set of Z on E. The uniform upper bounds for multi-parameter processes with independent increments under general conditions are also given. Most conclusions about uniform dimension can be considered as special cases of our results.

关 键 词：UNIFORM DIMENSION processes with INDEPENDENT INCREMENTS STABLE (N d α)-process. 

分 类 号：O211.6[理学—概率论与数理统计]