A method to compute the transition function of a piecewise deterministic Markov process with application to reliability

被引：19

作者：

Chiquet, Julien ^{[1
]}

Limnios, Nikolaos ^{[1
]}

机构：

[1] Univ Technol Compiegne, Lab Math Appl Compiegne, F-60206 Compiegne, France

来源：

STATISTICS & PROBABILITY LETTERS | 2008年 / 78卷 / 12期

关键词：

D O I：

10.1016/j.spl.2007.12.016

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：

We study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (MRP) associated to the PDMP and its Markov renewal equation (MRE) which is solved in order to obtain a closed-form solution of the transition function of the PDMP. It is then applied in the framework of survival analysis to evaluate the reliability function of a given system. We give a numerical illustration and we compare this analytical solution with the Monte Carlo estimator. (C) 2007 Elsevier B.V. All rights reserved.

引用

页码：1397 / 1403

页数：7

共 11 条

[1]

[Anonymous], 1993, MONOGR STAT APPL PRO, DOI DOI 10.1201/9780203748039

[2]

CHIQUET J, 2008, MATH METHOD IN PRESS

[3] Estimating stochastic dynamical systems driven by a continuous-time jump Markov process [J].

Chiquet, Julien ;

Limnios, Nikolaos .

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2006, 8 (04) :431-447

[4]

DAVIS MHA, 1984, J ROY STAT SOC B MET, V46, P353

[5] Probabilistic dynamics as a tool for dynamic PSA [J].

Devooght, J ;

Smidts, C .

RELIABILITY ENGINEERING & SYSTEM SAFETY, 1996, 52 (03) :185-196

[6]

Embrechts P, 2001, HANDB STAT, V19, P365, DOI 10.1016/S0169-7161(01)19014-0

[7]

Jacobsen, 2006, PROB APPLIC

[8]

Koroliuk VS, 2005, STOCHASTIC SYSTEMS IN MERGING PHASE SPACE, P1, DOI 10.1142/9789812703125

[9]

Lapeyre B., 2003, INTRO MONTE CARLO ME

[10]

Limnios N., 2001, An, Semi-Markov processes and reliability

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