Lattice semicontinuous poisson processes on Markov chains

1988 ◽  
Vol 39 (6) ◽  
pp. 573-576
Author(s):  
D. V. Gusak ◽  
A. I. Tureniyazova
Keyword(s):  
Markov Chains ◽  
Poisson Processes

On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions

1996 ◽  
Vol 33 (3) ◽  
pp. 640-653 ◽  
Author(s):  
Tobias Rydén
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Poisson Processes ◽  
Hitting Times ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Minimum Number ◽  
Markov Modulated ◽  
Two Parameters

An aggregated Markov chain is a Markov chain for which some states cannot be distinguished from each other by the observer. In this paper we consider the identifiability problem for such processes in continuous time, i.e. the problem of determining whether two parameters induce identical laws for the observable process or not. We also study the order of a continuous-time aggregated Markov chain, which is the minimum number of states needed to represent it. In particular, we give a lower bound on the order. As a by-product, we obtain results of this kind also for Markov-modulated Poisson processes, i.e. doubly stochastic Poisson processes whose intensities are directed by continuous-time Markov chains, and phase-type distributions, which are hitting times in finite-state Markov chains.

On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions

1996 ◽  
Vol 33 (03) ◽  
pp. 640-653 ◽  
Author(s):  
Tobias Rydén
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Poisson Processes ◽  
Hitting Times ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Minimum Number ◽  
Markov Modulated ◽  
Two Parameters

An aggregated Markov chain is a Markov chain for which some states cannot be distinguished from each other by the observer. In this paper we consider the identifiability problem for such processes in continuous time, i.e. the problem of determining whether two parameters induce identical laws for the observable process or not. We also study the order of a continuous-time aggregated Markov chain, which is the minimum number of states needed to represent it. In particular, we give a lower bound on the order. As a by-product, we obtain results of this kind also for Markov-modulated Poisson processes, i.e. doubly stochastic Poisson processes whose intensities are directed by continuous-time Markov chains, and phase-type distributions, which are hitting times in finite-state Markov chains.

Markov models—Markov chains

2019 ◽  
Vol 16 (8) ◽  
pp. 663-664 ◽  
Author(s):  
Jasleen K. Grewal ◽  
Martin Krzywinski ◽  
Naomi Altman
Keyword(s):  
Markov Chains ◽  
Markov Models
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