数学物理学报(英文版)

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UNIFORM PACKING DIMENSION RESULTS FOR MULTIPARAMETER STABLE PROCESSES

钟玉泉; 胡迪鹤   

  1. 中国科学院应用数学研究所, 北京 100080; 攀枝花大学理学院, 攀枝花 617000
  • 收稿日期:2004-04-09 修回日期:2005-01-08 出版日期:2007-01-20 发布日期:2007-01-20
  • 通讯作者: 钟玉泉
  • 基金资助:

    Supported by the National Natural Science Foundation of China.

UNIFORM PACKING DIMENSION RESULTS FOR MULTIPARAMETER STABLE PROCESSES

Zhong Yuquan; Hu Dihe   

  1. nstitute of Applied Mathematics, Academia Sinica, Beijing 100080, ChinaDepartment of Science, Panzhihua University, Panzhihua 617000, China
  • Received:2004-04-09 Revised:2005-01-08 Online:2007-01-20 Published:2007-01-20
  • Contact: Zhong Yuquan

摘要:

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 EB(RN+),
where Z(E)={x:\e t E, Z(t)=x}. Dim(E) denotes the acking dimension of E.

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

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 EB(RN+),
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

中图分类号: 

  • 60G52