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.
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页码：1737 / 1754
页数：18
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