The first-passage times of phase semi-Markov processes

2012 ◽  
Vol 82 (1) ◽  
pp. 40-48 ◽  
Author(s):  
Xuan Zhang ◽  
Zhenting Hou
Keyword(s):  
Markov Processes ◽  
First Passage Times ◽  
First Passage ◽  
Semi Markov Processes ◽  
Passage Times

First passage times and lumpability of semi-Markov processes

1988 ◽  
Vol 25 (04) ◽  
pp. 675-687 ◽  
Author(s):  
Ushio Sumita ◽  
Maria Rieders
Keyword(s):  
Markov Processes ◽  
First Passage Times ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Passage ◽  
The Laplace Transform ◽  
First Exit Times ◽  
Semi Markov Processes ◽  
Necessary And Sufficient ◽  
Passage Times

A necessary and sufficient condition of Serfozo (1971) for lumpability of semi-Markov processes is reinterpreted in terms of first-exit times. Furthermore, a new necessary and sufficient condition is developed by establishing relationships between first-passage times and lumpability of semi-Markov processes. The approach taken in this paper is entirely based on the Laplace-transform domain.

First passage times and lumpability of semi-Markov processes

1988 ◽  
Vol 25 (4) ◽  
pp. 675-687 ◽  
Author(s):  
Ushio Sumita ◽  
Maria Rieders
Keyword(s):  
Markov Processes ◽  
First Passage Times ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Passage ◽  
The Laplace Transform ◽  
First Exit Times ◽  
Semi Markov Processes ◽  
Necessary And Sufficient ◽  
Passage Times

A necessary and sufficient condition of Serfozo (1971) for lumpability of semi-Markov processes is reinterpreted in terms of first-exit times. Furthermore, a new necessary and sufficient condition is developed by establishing relationships between first-passage times and lumpability of semi-Markov processes. The approach taken in this paper is entirely based on the Laplace-transform domain.

On first-passage times in increasing Markov processes

1996 ◽  
Vol 26 (3) ◽  
pp. 199-203 ◽  
Author(s):  
Rafael Pérez-Ocón ◽  
M.Luz Gámiz-Pérez
Keyword(s):  
Markov Processes ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

Ageing first-passage times of Markov processes: a matrix approach

1997 ◽  
Vol 34 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Haijun Li ◽  
Moshe Shaked
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Critical Value ◽  
First Passage Times ◽  
Matrix Approach ◽  
First Passage ◽  
Passage Times

Using a matrix approach we discuss the first-passage time of a Markov process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first-passage time possesses various ageing properties are studied. Some results previously obtained by Li and Shaked (1995) are extended.

Processes with new better than used first-passage times

1984 ◽  
Vol 16 (03) ◽  
pp. 667-686 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Point Process ◽  
Markov Processes ◽  
Probability Space ◽  
Sufficient Conditions ◽  
General Point ◽  
First Passage ◽  
Semi Markov Processes ◽  
New Better Than Used ◽  
Better Than ◽  
Passage Times

Let with Z(0) = 0 be a random process under investigation and N be a point process associated with Z. Both Z and N are defined on the same probability space. Let with R 0 = 0 denote the consecutive positions of points of N on the half-line . In this paper we present sufficient conditions under which (Z, R) is a new better than used (NBU) process and give several examples of NBU processes satisfying these conditions. In particular we consider the processes in which N is a renewal and a general point process. The NBU property of some semi-Markov processes is also presented.

On ageing properties of first-passage times of increasing Markov processes

2002 ◽  
Vol 34 (01) ◽  
pp. 241-259
Author(s):  
Félix Belzunce ◽  
Eva-María Ortega ◽  
José M. Ruiz
Keyword(s):  
Markov Chain ◽  
Markov Processes ◽  
Continuous Time ◽  
Transition Matrix ◽  
Sufficient Conditions ◽  
First Passage Times ◽  
Generator Matrix ◽  
First Passage ◽  
Finite Case ◽  
Passage Times

The purpose of this paper is to study ageing properties of first-passage times of increasing Markov chains. We extend the literature to some new ageing classes, such as the IFR(2), NBU(2), DRLLt and NBULt classes. We also give sufficient conditions in the finite case, that are more efficient computationally, just in terms of the transition matrix K, in the discrete case, or the generator matrix Q, in the continuous case. For the uniformizable, continuous-time Markov processes, we derive conditions in terms of the discrete uniformized Markov chain for the NBU(2) and the NBULt classes. In the last section, a review of the main results in this direction in the literature is given, and we compare some of the conditions stated in this paper with others given in the literature about some other ageing classes. Some examples where these results are applied are given.

Sign in / Sign up

Export Citation Format

Share Document