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...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.展开更多
基金Project supported by Fujian Natural Science Foundation.
文摘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.
