Some passage-time generating functions for discrete-time and continuous-time finite Markov chains
- 1 August 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 4 (03) , 496-507
- https://doi.org/10.1017/s002190020002550x
Abstract
Let T denote a subset of the possible transitions between the states of a finite Markov chain and let Yk denote the time of the kth occurrence of a T-transition. Formulae are derived for the generating functions of Yk , of Yj + k — Yj and of Yj + k — Yj in the limit as j → ∞, for both discrete-time and continuoustime chains. Several particular cases are briefly discussed.Keywords
This publication has 1 reference indexed in Scilit:
- Identities for passage times with applications to recurrent events and homogeneous differential functionsJournal of Applied Probability, 1966