FIRST-PASSAGE TIMES FOR SOME LINDLEY PROCESSES IN CONTINUOUS TIME

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.

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Exponentiality of First Passage Times of Continuous Time Markov Chains

Acta Applicandae Mathematicae ◽

10.1007/s10440-013-9854-z ◽

2013 ◽

Vol 131 (1) ◽

pp. 197-212 ◽

Cited By ~ 1

Author(s):

Romain Bourget ◽

Loïc Chaumont ◽

Natalia Sapoukhina

Keyword(s):

Markov Chains ◽

Continuous Time ◽

First Passage Times ◽

First Passage ◽

Continuous Time Markov Chains ◽

Passage Times

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

Advances in Applied Probability ◽

10.1239/aap/1019160959 ◽

2002 ◽

Vol 34 (1) ◽

pp. 241-259 ◽

Cited By ~ 1

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.

Download Full-text