广义α-Stable过程的像集和图集的一致维数

Uniform Dimension of N-Parameter d-Dimensional Generalized α-Stable Process

研究了未必具有随机一致Holder条件的N指标d维广义α-stable过程的像集和图集的一致维数问题,并在一定条件下得到了N指标d维广义α-stable过程像集约一致Hausdorff维数和一致Packing维数的上、下界,图集的一致Hausdorff维数和一致Packing维数的上界,包含了多指标α-stable过程和广义布朗单相应的结果．

The problem of the uniform dimensions for image sets and graph sets of N-parameter d-dimensional generalized α-stable process, which may not possess the uniform stochastic HSlder condition, is investigated. The uniform Hausdorff dimension and the uniform Packing dimension for image sets of N-parameter α-dimensional gen- eralized α-stable process are obtained, and the upper bounds of the uniform Hausdorff dimension and the uniform Packing dimension for graph sets are also given, the results contain the results of multi-parameter stable processes and generalized Brownian sheet.