An alternative approach to the analysis of finite semi-markov and related processes
- 1 January 1987
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 3 (1) , 67-87
- https://doi.org/10.1080/15326348708807047
Abstract
Let J(t) be a finite semi-Markov process associated with the age process X(t) and the reward process Z(t). Bystudying the probabilistic flow of the trivariate process in its state space, new transform results are obtained. Some known results are then derived directly from these transform results, thereby providing an alternative approach for analysis of semi-Markov and related processes. Some new results are also obtained regarding the reward process Z(t) and its first passage times.Keywords
This publication has 22 references indexed in Scilit:
- The bivariate Laguerre transform and its applications: numerical exploration of bivariate processesAdvances in Applied Probability, 1985
- A process by chain dependent growth rate. part II: The ruin and ergodic problemsAdvances in Applied Probability, 1971
- Markov renewal theoryAdvances in Applied Probability, 1969
- On the moments of Markov renewal processesAdvances in Applied Probability, 1969
- Exponential ergodicity in Markov renewal processesJournal of Applied Probability, 1968
- The Existence and Uniqueness of Stationary Measures for Markov Renewal ProcessesThe Annals of Mathematical Statistics, 1966
- Limit Theorems for Markov Renewal ProcessesThe Annals of Mathematical Statistics, 1964
- A central limit theorem for processes defined on a finite Markov chainMathematical Proceedings of the Cambridge Philosophical Society, 1964
- Markov Renewal Processes with Finitely Many StatesThe Annals of Mathematical Statistics, 1961
- Markov Renewal Processes: Definitions and Preliminary PropertiesThe Annals of Mathematical Statistics, 1961