Stable Processes with Stationary Increments Parameterized by Metric Spaces

被引：5

作者：

Fu, Zuopeng ^{[1
]}

Wang, Yizao ^{[1
]}

机构：

[1] Univ Cincinnati, Dept Math Sci, 2815 Commons Way, Cincinnati, OH 45221 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2020年 / 33卷 / 03期

关键词：

Levy Brownian field; Set-indexed process; Stable process; Stationary increment; Chentsov representation; Measure definite kernel; BROWNIAN-MOTION; DEFINITE KERNELS; RANDOM-FIELDS;

D O I：

10.1007/s10959-019-00912-1

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A new family of stable processes indexed by metric spaces with stationary increments is introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a result on the so-called measure definite kernels is of independent interest. A limit theorem for set-indexed processes is also established.

引用

页码：1737 / 1754

页数：18

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