Sharp asymptotics of large deviations for general state-space Markov-additive chains in Rd

被引：7

作者：

Iltis, M ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2000年 / 47卷 / 04期

关键词：

asymptotic expansion; large deviations; rate function; Markov-additive random variables; general state-space Markov chain; regenerative process;

D O I：

10.1016/S0167-7152(99)00181-9

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 {xi(i)} subset of R-d, i = 0, 1, 2, .... Markov-additive (MA) random variables, d greater than or equal to 2, S-n = Sigma(i)(= 0)(n) xi(i), and (X-n, S-n) a phi-irreducible, aperiodic, time-homogeneous MA-chain, a = inf(x epsilon) r I(x), we extend to general state-space chains, under a regeneration hypothesis, asymptotic results of the form P(S-n epsilon n Gamma;X-n epsilon A) = n(V)e(-na)(d(0) + o(l)) as n --> infinity. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：365 / 380

页数：16

共 15 条

[1]

Bhattacharya RN., 1976, NORMAL APPROXIMATION

[2] THE BERRY-ESSEEN THEOREM FOR FUNCTIONALS OF DISCRETE MARKOV-CHAINS [J].

BOLTHAUSEN, E .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1980, 54 (01) :59-73

[3] THE BERRY-ESSEEN THEOREM FOR STRONGLY MIXING HARRIS RECURRENT MARKOV-CHAINS [J].

BOLTHAUSEN, E .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1982, 60 (03) :283-289

[4] Sharp asymptotics of large deviations in R(d) [J].

Iltis, M .

JOURNAL OF THEORETICAL PROBABILITY, 1995, 8 (03) :501-522

[5]

ILTIS MG, 1998, SHARP ASYMPTOTICS LA

[6]

ISCOE I, 1985, ADV APPL MATH, V6, P373, DOI 10.1016/0196-8858(85)90017-X

[7]

Jensen J.L., 1995, SADDLEPOINT APPROXIM

[8] SADDLEPOINT EXPANSIONS FOR SUMS OF MARKOV DEPENDENT-VARIABLES ON A CONTINUOUS STATE-SPACE [J].

JENSEN, JL .

PROBABILITY THEORY AND RELATED FIELDS, 1991, 89 (02) :181-199

[9]

JENSEN JL, 1989, SCAND J STAT, V16, P47

[10] A NOTE ON ASYMPTOTIC EXPANSIONS FOR MARKOV-CHAINS USING OPERATOR-THEORY [J].

JENSEN, JL .

ADVANCES IN APPLIED MATHEMATICS, 1987, 8 (04) :377-392

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