TRANSITION PHENOMENA FOR LADDER EPOCHS OF RANDOM WALKS WITH SMALL NEGATIVE DRIFT

被引：0

作者：

Wachtel, Vitali ^{[1
]}

机构：

[1] Univ Munich, Math Inst, D-80333 Munich, Germany

来源：

ADVANCES IN APPLIED PROBABILITY | 2009年 / 41卷 / 04期

关键词：

Random walk; ladder epoch; transition phenomena; LARGE DEVIATIONS; LIMIT-THEOREMS; FLUCTUATION; SUMS;

D O I：

10.1239/aap/1261669592

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：

For a family of random walks {S-(a)} satisfying E S-1((a)) = -a < 0, we consider ladder epochs tau((a)) = min{k >= 1: S-k((a)) < 0}. We study the asymptotic behaviour, as a -> 0, of P(tau((a)) > n) in the case when n = n(a) -> infinity. As a consequence, we also obtain the growth rates of the moments of tau((a)).

引用

页码：1189 / 1214

页数：26

共 17 条

[1] Some asymptotic results for transient random walks [J].

Bertoin, J ;

Doney, RA .

ADVANCES IN APPLIED PROBABILITY, 1996, 28 (01) :207-226

[2] CONDITIONAL LIMIT-THEOREMS FOR ASYMPTOTICALLY STABLE RANDOM-WALKS [J].

DONEY, RA .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1985, 70 (03) :351-360

[3] ON THE ASYMPTOTIC-BEHAVIOR OF 1ST PASSAGE TIMES FOR TRANSIENT RANDOM-WALK [J].

DONEY, RA .

PROBABILITY THEORY AND RELATED FIELDS, 1989, 81 (02) :239-246

[4]

EMBRECHTS P, 1982, J AUST MATH SOC A, V32, P412, DOI 10.1017/S1446788700024976

[5]

Feller W., 1971, An Introduction to Probability Theory and its Applications - volume two, VII

[6] MOMENTS AND LIMIT DISTRIBUTIONS OF SOME FIRST PASSAGE TIMES [J].

GUT, A .

ANNALS OF PROBABILITY, 1974, 2 (02) :277-308

[7] FIRST PASSAGE TIME DENSITY FOR HOMOGENEOUS SKIP-FREE WALKS ON CONTINUUM [J].

KEILSON, J .

ANNALS OF MATHEMATICAL STATISTICS, 1963, 34 (03) :1003-&

[8] On the mean value of the ladder epoch for random walks with a small drift [J].

Lotov, V. I. .

IZVESTIYA MATHEMATICS, 2006, 70 (06) :1225-1232

[9]

Nagaev A. V., 1969, Izv. Akad. Nauk UzSSR, Ser. Fiz.- Mat. Nauk, V6, P17

[10] LARGE DEVIATIONS OF SUMS OF INDEPENDENT RANDOM-VARIABLES [J].

NAGAEV, SV .

ANNALS OF PROBABILITY, 1979, 7 (05) :745-789

← 1 2 →