Ergodic properties of max-infinitely divisible processes

被引：31

作者：

Kabluchko, Zakhar ^{[1
]}

Schlather, Martin ^{[1
]}

机构：

[1] Inst Math Stochastik, D-37077 Gottingen, Germany

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 03期

关键词：

Max-infinitely divisible processes; Max-stable processes; Ergodicity; Mixing; Codifference; SAMPLE;

D O I：

10.1016/j.spa.2009.12.002

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：

We prove that a stationary max-infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesaro summable to 0). These criteria are applied to some classes of max-infinitely divisible processes. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：281 / 295

页数：15

共 32 条

[1] [Anonymous], 1984, GRAD TEXTS MATH
[2] [Anonymous], 1987, APPL PROBABILITY
[3] [Anonymous], 1982, GRUNDLEHREN MATH WIS
[4] MAX-INFINITE DIVISIBILITY
BALKEMA, AA
RESNICK, SI
[J]. JOURNAL OF APPLIED PROBABILITY, 1977, 14 (02) : 309 - 319
[5] ERGODIC PROPERTIES OF STATIONARY STABLE PROCESSES
CAMBANIS, S
HARDIN, CD
WERON, A
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1987, 24 (01) : 1 - 18
[6] DEHAAN L, 1984, ANN PROBAB, V12, P1194
[7] DEHAAN L, 1985, B INT STAT I, V51
[8] DEOLIVEIRA JT, 1962, ESTUDOS MATH ESTAT E, V7, P165
[9] MAX-INFINITELY DIVISIBLE AND MAX-STABLE SAMPLE CONTINUOUS-PROCESSES
GINE, E
HAHN, MG
VATAN, P
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1990, 87 (02) : 139 - 165
[10] ERGODIC PROPERTIES OF RANDOM MEASURES ON STATIONARY-SEQUENCES OF SETS
GROSS, A
ROBERTSON, JB
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1993, 46 (02) : 249 - 265

← 1 2 3 4 →