The local times and Hausdorff measure for level sets of a Wiener sheet

被引：0

作者：

林火南

机构：

来源：

ScienceinChina,SerA. | 2001年 / Ser.A.2001卷 / 06期

关键词：

D O I：

暂无

中图分类号：

O189 [拓扑（形势几何学）];

学科分类号：

070104 ;

摘要：

<正>In this paper, we discuss the relation between the local times and the level sets of a Wiener sheet, and give moment estimates for the local times of a Wiener sheet. We show that the correct Hausdorff measure function for level sets of N-parameter Rσ-valued Wiener sheet is φ ( r) = rN-d/2(loglog1/r)d/2 if 2N> d. This solves the problem posed by S. J. Taylor.

引用

页码：696 / 708

页数：13

共 5 条

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[2] Sample function properties of multi-parameter stable processes[J] W. Ehm Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1981, 2
[3] OCCUPATION DENSITIES
GEMAN, D
HOROWITZ, J
[J]. ANNALS OF PROBABILITY, 1980, 8 (01) : 1 - 67
[4] Local Holder Conditions for the Local Times of Certain Stationary Gaussian Processes[J] Laurie Davies The Annals of Probability 1976, 2
[5] Sample Functions of the $N$-Parameter Wiener Process[J] Steven Orey;William E. Pruitt The Annals of Probability 1973, 1

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