Journal ArticleDOI
An alternative approach to the analysis of finite semi-markov and related processes
Sumita Ushio,Masuda Yasushi +1 more
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In this article, a finite semi-Markov process associated with the age process X(t) and the reward process Z(t), and its first passage times are derived by studying the probabilistic flow of the trivariate process in its state space.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.read more
Citations
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Two Types of RG-Factorizations of Quasi-birth-and-death Processes and Their Applications to Stochastic Integral Functionals
Quan-Lin Li,Jinhua Cao +1 more
TL;DR: In this paper, UL-and LU-type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely many levels or infinitely many levels were provided.
Journal ArticleDOI
Continuous-time markov chains in a random environment, with applications to ion channel modelling
TL;DR: In this paper, the authors studied a bivariate stochastic process where the channel process is a continuous-time Markov chain with infinitesimal generator at time t dependent on XE (t) and the environment process is not dependent on Z(t).
Journal ArticleDOI
A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions
Yasushi Masuda,Ushio Sumita +1 more
TL;DR: In this paper, a multivariate reward process defined on a semi-Markov process is studied, and transform results for the distributions of the reward and related processes are derived through the method of supplementary variables and the Markov renewal equations.
Journal ArticleDOI
Reward processes for semi-markov processes: asymptotic behaviour
A. Reza Soltani,K. Khorshidian +1 more
TL;DR: The asymptotic behavior of the cumulative mean of a reward process, where the reward function ρ belongs to a rather large class of functions, is studied in this paper.
References
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Regenerative Stochastic Processes
TL;DR: In this article, a wide class of stochastic processes, called regenerative, is defined, and it is shown that under general conditions the instantaneous probability distribution of such a process tends with time to a unique limiting distribution, whatever the initial conditions.
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Markov renewal processes: Definitions and preliminary properties
TL;DR: In this paper, a classification of the states of a Markov Renewal process is described and studied, and the concept of regularity is introduced and characterized, and some preliminary results on Markov renewal processes and Semi-Markov processes are given.
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Markov Renewal Processes with Finitely Many States
TL;DR: In this article, the authors studied Markov renewal processes with a finite number of states and derived explicit expressions for the distribution functions of first passage times, as well as for the marginal distribution function of the corresponding Semi-Markov process.
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Markov renewal theory
TL;DR: In this paper, the authors consider a stochastic process X(t) (t ≧ 0) taking values in a countable state space, where a particle moves from state to state in such a way that the successive states visited form a Markov chain, and the particle stays in a given state a random amount of time depending on the state it is in as well as on the next state to be visited next.