On the Existence and Uniqueness of Solution of MRE and Applications

被引：4

作者：

Hou, Yunhui ^{[1
]}

Limnios, Nikolaos ^{[2
]}

Schon, Walter ^{[1
]}

机构：

[1] Univ Technol Compiegne, Sorbonne Univ, CNRS, UMR Heudiasyc 7253, CS 60 319, F-60203 Compiegne, France

[2] Univ Technol Compiegne, Sorbonne Univ, LMAC, CS 60 319, F-60203 Compiegne, France

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2017年 / 19卷 / 04期

关键词：

Semi-Markov process; Markov renewal equation; Semi-Markov chain; Semi-Markov transition function;

D O I：

10.1007/s11009-017-9570-7

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：

In this paper, we study the existence and uniqueness of the solution for Markov renewal equation (MRE) of a semi-Markov process with countable state space. This method and its proof are based on an iterative scheme. A numerical solution is also given as well as a case study on system reliability assessment.

引用

页码：1241 / 1250

页数：10

共 14 条

[1]

[Anonymous], 2008, LECT NOTES STAT

[2] Numerical treatment of homogeneous semi-Markov processes in transient case - A straightforward approach [J].

Corradi, G ;

Janssen, J ;

Manca, R .

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2004, 6 (02) :233-246

[3]

Cox DR, 2008, MATH P CAMB PHILOS S, V51, P433

[4] Age-usage semi-Markov models [J].

D'Amico, Guglielmo .

APPLIED MATHEMATICAL MODELLING, 2011, 35 (09) :4354-4366

[5] On Numerical Solution of the Markov Renewal Equation: Tight Upper and Lower Kernel Bounds [J].

D. A. Elkins ;

M. A. Wortman .

Methodology And Computing In Applied Probability, 2001, 3 (3) :239-253

[6]

Gikhman II, 1974, THEORY STOCHASTIC PR, V2

[7]

Grabski F, 2007, RELIAB THEORY APPL, V3-4, P60

[8]

Janssen J., 2007, Semi-Markov Risk Models fo Finance, Insurance and Reliability

[9]

Korolyuk VS, 1966, CYBERNETICS, V1, P58

[10] Interval Reliability, Corrections and Developments of "Reliability Measures of Semi-Markov Systems with General State Space" [J].

Limnios, Nikolaos .

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2014, 16 (03) :765-770

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