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

共 50 条

[1] Stable Processes with Stationary Increments Parameterized by Metric Spaces
Zuopeng Fu
Yizao Wang
Journal of Theoretical Probability, 2020, 33 : 1737 - 1754
[2] PROCESSES WITH STATIONARY INCREMENTS
PICINBONO, B
ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS, 1975, 30 (7-8): : 211 - 212
[3] A class of asymptotically self-similar stable processes with stationary increments
Can, Sami Umut
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2014, 124 (12) : 3986 - 4011
[4] 2 CLASSES OF SELF-SIMILAR STABLE PROCESSES WITH STATIONARY INCREMENTS
CAMBANIS, S
MAEJIMA, M
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 32 (02) : 305 - 329
[5] Maxima of long memory stationary symmetric α-stable processes, and self-similar processes with stationary max-increments
Owada, Takashi
Samorodnitsky, Gennady
BERNOULLI, 2015, 21 (03) : 1575 - 1599
[6] (1/ALPHA)-SELF SIMILAR ALPHA-STABLE PROCESSES WITH STATIONARY INCREMENTS
SAMORODNITSKY, G
TAQQU, MS
JOURNAL OF MULTIVARIATE ANALYSIS, 1990, 35 (02) : 308 - 313
[7] A note on processes with random stationary increments
Zhang, Haimeng
Huang, Chunfeng
STATISTICS & PROBABILITY LETTERS, 2014, 94 : 153 - 161
[8] VARIATIONS OF PROCESSES WITH STATIONARY, INDEPENDENT INCREMENTS
GREENWOOD, P
FRISTEDT, B
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1972, 23 (03): : 171 - +
[9] PROCESSES WITH CONDITIONAL STATIONARY INDEPENDENT INCREMENTS
SERFOZO, RF
JOURNAL OF APPLIED PROBABILITY, 1972, 9 (02) : 303 - &
[10] TRANSITION DENSITY ESTIMATES FOR RELATIVISTIC α-STABLE PROCESSES ON METRIC SPACES
Balsam, Hubert
Pietruska-Paluba, Katarzyna
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2020, 40 (02): : 183 - 204

← 1 2 3 4 5 →