Simulating tail asymptotics of a Markov chain

被引：0

作者：

Khanchi, Aziz ^{[1
]}

Lamothe, Gilles ^{[2
]}

机构：

[1] Univ Ottawa, Sch Informat Technol & Engn, Ottawa, ON K1N 6N5, Canada

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

来源：

STATISTICS & PROBABILITY LETTERS | 2011年 / 81卷 / 09期

关键词：

Rare event simulation; Time reversed Markov chain; Jackson network; Strongly consistent estimator; STABLE STOCHASTIC SYSTEMS; EXCESSIVE BACKLOGS; LARGE DEVIATIONS; NETWORKS; QUEUES; DECAY;

D O I：

10.1016/j.spl.2011.04.006

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：

This paper develops a rare event simulation algorithm for a discrete-time Markov chain in the first orthant. The algorithm gives a very good estimate of the stationary distribution along one of the axes and it is shown to be efficient. A key idea is to study an associated time reversed Markov chain that starts at the rare event. We will apply the algorithm to a Markov chain related to a Jackson network with two stations. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：1392 / 1397

页数：6

共 50 条

[1] ASYMPTOTICS OF MARKOV KERNELS AND THE TAIL CHAIN
Resnick, Sidney I.
Zeber, David
ADVANCES IN APPLIED PROBABILITY, 2013, 45 (01) : 186 - 213
[2] TAIL FIELD OF A MARKOV CHAIN
ABRAHAMSE, AF
ANNALS OF MATHEMATICAL STATISTICS, 1969, 40 (01): : 127 - +
[3] Asymptotics for Markov chain mixture detection
Fitzpatrick, Matthew
Stewart, Michael
ECONOMETRICS AND STATISTICS, 2022, 22 : 56 - 66
[4] TAIL EVENTS OF A MARKOV-CHAIN
COHN, H
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1974, 29 (01): : 65 - 72
[5] The Markov chain asymptotics of random mapping graphs
Chen, Xinxing
Ying, Jiangang
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2007, 43 (03): : 353 - 374
[6] Tail asymptotics of a Markov-modulated infinite-server queue
Blom, J.
De Turck, K.
Kella, O.
Mandjes, M.
QUEUEING SYSTEMS, 2014, 78 (04) : 337 - 357
[7] Tail asymptotics of a Markov-modulated infinite-server queue
J. Blom
K. De Turck
O. Kella
M. Mandjes
Queueing Systems, 2014, 78 : 337 - 357
[8] Markov modulated fluid network process: Tail asymptotics of the stationary distribution
Miyazawa, Masakiyo
STOCHASTIC MODELS, 2020, 37 (01) : 127 - 167
[9] Asymptotics of a matrix valued Markov chain arising in sociology
Bonacich, P
Liggett, TM
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 104 (01) : 155 - 171
[10] Exact asymptotics for the stationary distribution of a Markov chain: a production model
Ivo Adan
Robert D. Foley
David R. McDonald
Queueing Systems, 2009, 62 : 311 - 344

← 1 2 3 4 5 →