Abstract:

In this article, authors discuss the problem of uniform packing dimension of the image set of multiparameter stochastic processes without random uniform H\"older condition, and obtain the uniform packing dimension of multiparameter stable processes. If Z is a stable (N,d,α)-process and αN ≤ d, then the following holds with probability 1
Dim Z(E) = α Dim E for any Borel set E∈ B(R^N₊),
where Z(E)={x:\e t∈ E, Z(t)=x}. Dim(E) denotes the acking dimension of E.

Key words: (N,d,α)-stable process, stopping time, Kolmogorov upper index, packing dimension