On the Limiting Joint Distribution of Semi-Markov Processes with Finite Number of States, with an Application

Charles S. Bakheit; Elfadl K. Elsheikh

On the Limiting Joint Distribution of Semi-Markov Processes with Finite Number of States, with an Application

Charles S. Bakheit^*, Elfadl K. Elsheikh

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive expressions for lim_{t → ∞} Prob {Z_t = i, Z_t+z = j} for a semi-Markov process with a finite number of states. As an application of the resuts, we obtain the autocorrelation function of the process of recorded current flowing through a single channel, for two Markovian models of the behavior of drug-operated ion-channels. The additional information provided by the autocorrelation function would facilitate the task of identifying the model which is more consistent with the observed record.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Arab Gulf Journal of Scientific Research
Volume	17
Issue number	1
Publication status	Published - Apr 1999

Keywords

Autocorrelation function
Ion-channels
Renewal processes
Semi-Markov processes

ASJC Scopus subject areas

Ecology, Evolution, Behavior and Systematics
Agronomy and Crop Science
Water Science and Technology

Cite this

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title = "On the Limiting Joint Distribution of Semi-Markov Processes with Finite Number of States, with an Application",

abstract = "We derive expressions for limt → ∞ Prob {Zt = i, Zt+z = j} for a semi-Markov process with a finite number of states. As an application of the resuts, we obtain the autocorrelation function of the process of recorded current flowing through a single channel, for two Markovian models of the behavior of drug-operated ion-channels. The additional information provided by the autocorrelation function would facilitate the task of identifying the model which is more consistent with the observed record.",

keywords = "Autocorrelation function, Ion-channels, Renewal processes, Semi-Markov processes",

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year = "1999",

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N2 - We derive expressions for limt → ∞ Prob {Zt = i, Zt+z = j} for a semi-Markov process with a finite number of states. As an application of the resuts, we obtain the autocorrelation function of the process of recorded current flowing through a single channel, for two Markovian models of the behavior of drug-operated ion-channels. The additional information provided by the autocorrelation function would facilitate the task of identifying the model which is more consistent with the observed record.

AB - We derive expressions for limt → ∞ Prob {Zt = i, Zt+z = j} for a semi-Markov process with a finite number of states. As an application of the resuts, we obtain the autocorrelation function of the process of recorded current flowing through a single channel, for two Markovian models of the behavior of drug-operated ion-channels. The additional information provided by the autocorrelation function would facilitate the task of identifying the model which is more consistent with the observed record.

KW - Autocorrelation function

KW - Ion-channels

KW - Renewal processes

KW - Semi-Markov processes

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On the Limiting Joint Distribution of Semi-Markov Processes with Finite Number of States, with an Application

Abstract

Keywords

ASJC Scopus subject areas

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