THE EXTREMAL INDEX FOR A MARKOV-CHAIN

被引：67

作者：

SMITH, RL ^{[1
]}

机构：

[1] UNIV SURREY,GUILDFORD GU2 5XH,SURREY,ENGLAND

来源：

JOURNAL OF APPLIED PROBABILITY | 1992年 / 29卷 / 01期

关键词：

HARRIS CHAINS; MULTIVARIATE EXTREME VALUE DISTRIBUTIONS; WIENER-HOPF INTEGRAL EQUATION;

D O I：

10.2307/3214789

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：

The paper presents a method of computing the extremal index for a discrete-time stationary Markov chain in continuous state space. The method is based on the assumption that bivariate margins of the process are in the domain of attraction of a bivariate extreme value distribution. Scaling properties of bivariate extremes then lead to a random walk representation for the tail behaviour of the process, and hence to computation of the extremal index in terms of the fluctuation properties of that random walk. The result may then be used to determine the asymptotic distribution of extreme values from the Markov chain.

引用

页码：37 / 45

页数：9

共 16 条

[1] AN EXTREMAL MARKOVIAN SEQUENCE [J].

ALPUIM, MT .

JOURNAL OF APPLIED PROBABILITY, 1989, 26 (02) :219-232

[2]

COLES SG, 1991, J ROY STAT SOC B MET, V53, P377

[3]

GRIMMETT G, 1982, PRROBABILITY RANDOM

[4]

JOE H, 1992, J ROY STAT SOC B MET, V54, P171

[5]

Krein M. G., 1962, T AM MATH SOC, V22, P163

[6] EXTREMAL THEORY FOR STOCHASTIC-PROCESSES [J].

LEADBETTER, MR ;

ROOTZEN, H .

ANNALS OF PROBABILITY, 1988, 16 (02) :431-478

[7] EXTREMES AND LOCAL DEPENDENCE IN STATIONARY-SEQUENCES [J].

LEADBETTER, MR .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1983, 65 (02) :291-306

[8] EXTREME VALUES IN UNIFORMLY MIXING STATIONARY STOCHASTIC-PROCESSES [J].

LOYNES, RM .

ANNALS OF MATHEMATICAL STATISTICS, 1965, 36 (03) :993-999

[9] ASYMPTOTIC EXTREMES FOR M-DEPENDENT RANDOM-VARIABLES [J].

NEWELL, GF .

ANNALS OF MATHEMATICAL STATISTICS, 1964, 35 (03) :1322-&

[10] MAXIMUM TERM OF UNIFORMLY MIXING STATIONARY PROCESSES [J].

OBRIEN, GL .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1974, 30 (01) :57-63

← 1 2 →