On the use of Cauchy integral formula for the embedding problem of discrete-time Markov chains

Ekhosuehi, Virtue U.

doi:10.1080/03610926.2021.1921806

Cited by 2 publications

(2 citation statements)

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“…The characterization of an embeddable stochastic matrix in a form useful for practical purposes was recently achieved in [43]. More useful results were obtained in [44]. The connections between this kind of embedding and the other approaches, for the association of a discrete time Markov chain and a continuous time process, deserve further study.…”

Section: The Embedding Of a Discrete Time Markov Chain In A Continuous Onementioning

confidence: 99%

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Open Markov Type Population Models: From Discrete to Continuous Time

2021

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We address the problem of finding a natural continuous time Markov type process—in open populations—that best captures the information provided by an open Markov chain in discrete time which is usually the sole possible observation from data. Given the open discrete time Markov chain, we single out two main approaches: In the first one, we consider a calibration procedure of a continuous time Markov process using a transition matrix of a discrete time Markov chain and we show that, when the discrete time transition matrix is embeddable in a continuous time one, the calibration problem has optimal solutions. In the second approach, we consider semi-Markov processes—and open Markov schemes—and we propose a direct extension from the discrete time theory to the continuous time one by using a known structure representation result for semi-Markov processes that decomposes the process as a sum of terms given by the products of the random variables of a discrete time Markov chain by time functions built from an adequate increasing sequence of stopping times.

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Section: The Embedding Of a Discrete Time Markov Chain In A Continuous Onementioning

confidence: 99%

“…Following the work in [45] (pp. [41][42][43][44], we consider the definition of an extended solution for a Cauchy problem of a differential equation,…”

Section: Continuous Time Markov Chains Calibration With a Discrete Time Markov Transition Matrixmentioning

confidence: 99%