STRONG APPROXIMATION OF THE NUMBER OF RENEWAL PACED RECORD TIMES

被引：1

作者：

ENNADIFI, G

机构：

[1] UNIV LYON 1,F-75252 PARIS 05,FRANCE

[2] UNIV PARIS 06,LSTA,F-75252 PARIS 05,FRANCE

[3] CNRS,URA 1321,F-75700 PARIS,FRANCE

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1995年 / 45卷 / 1-2期

关键词：

RECORD VALUES; RECORD TIMES; INTER-RECORD TIMES; RENEWAL PROCESS; MARKOV PROCESS; STRONG APPROXIMATIONS;

D O I：

10.1016/0378-3758(94)00066-2

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：

Let {Y-n, n greater than or equal to 0} be a sequence of independent and identically distributed random variables with continuous distribution function, and let {N(T), T greater than or equal to 0} be a renewal process independent of {Y-n n greater than or equal to 0}. We consider the process {H(T), T greater than or equal to 0} of the number of record times until time T of the renewal paced record process {X(T), T greater than or equal to 0} based on {Y-n, n greater than or equal to 0} and {N(T), T greater than or equal to 0}. We establish a strong invariance principle, and limit laws related to {H(T), T greater than or equal to 0}.

引用

页码：113 / 132

页数：20

共 63 条

[31] NON-HOMOGENEOUSLY PACED RANDOM RECORDS AND ASSOCIATED EXTREMAL PROCESSES
GAVER, DP
JACOBS, PA
[J]. JOURNAL OF APPLIED PROBABILITY, 1978, 15 (03) : 552 - 559
[32] CONVERGENCE-RATES FOR RECORD TIMES AND THE ASSOCIATED COUNTING PROCESS
GUT, A
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1990, 36 (01) : 135 - 151
[33] Hall P., 1982, RATES CONVERGENCE CE
[34] APPROXIMATION OF PARTIAL SUMS OF INDEPENDENT RV-S, AND SAMPLE DFI
KOMLOS, J
MAJOR, P
TUSNADY, G
[J]. ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1975, 32 (1-2): : 111 - 131
[35] ON DEPENDENT MARKING AND THINNING OF POINT-PROCESSES
LAST, G
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1993, 45 (01) : 73 - 94
[36] MASON D. M., 1987, PUBL I STAT U PARIS, V32, P81
[37] SOME LIMIT THEOREMS FOR LARGE DEVIATIONS
NAGAEV, SV
[J]. THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1965, 10 (02): : 214 - &
[38] RECORD VALUES AND RELATED STATISTICS - A REVIEW
NAGARAJA, HN
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1988, 17 (07) : 2223 - 2238
[39] NEVKZOROV VB, 1986, PROBAB THEORY MATH S, V2, P365
[40] NEVZOROV VB, 1987, VESTNIK LENINGRAD ST, V1, P33

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