Abstract
Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference56 articles.
1. Markov Renewal Processes with Finitely Many States
2. Introduction to Stochastic Processes;Cinlar,2013
3. Dynamic Probabilistic Systems: Semi-Markov and Decision Processes;Howard,2007
4. A semi-Markov model for a multigrade population with Poisson recruitment
5. Semi-Markov models for manpower planning;McClean,1986
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献