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A method for approximating the probability functions of a Markov chain

Published online by Cambridge University Press:  14 July 2016

Keith N. Crank
Keith N. Crank*
Affiliation:
Vanderbilt University
*
∗Postal address: Owen Graduate School of Management, Vanderbilt University, Nashville, TN 37203, USA.
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Abstract

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.

Keywords

RIGHT-SHIFT PROCESSKOLMOGOROV DIFFERENTIAL EQUATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 808 - 814
Copyright
Copyright © Applied Probability Trust 1988 

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References

Billard, L. (1973) Factorial moments and probabilities for the general stochastic epidemic. J. Appl. Prob. 10, 277–288.CrossRefGoogle Scholar
Billard, L. (1975) General stochastic epidemic with recovery. J. Appl. Prob. 12, 29–38.Google Scholar
Billard, L. (1976) A stochastic general epidemic in m sub-populations. J. Appl. Prob. 13, 567–572.Google Scholar
Billard, L. (1977) On Lotka–Volterra predator prey models. J. Appl. Prob. 14, 375–381.Google Scholar
Billard, L. (1981) Generalized two-dimensional bounded birth and death processes and some applications. J. Appl. Prob. 18, 335–347.Google Scholar
Billard, L. Kryscio, R. J. (1977) The transition probabilities of a bounded bivariate pure death process. Math. Biosci, 37, 205–221.Google Scholar
Kryscio, R. J. Severo, N. C. (1975) Computational and estimation procedures in multidimensional right-shift processes and some applications. Adv. Appl. Prob. 7, 349–382.Google Scholar
Puri, P. S. (1968) Interconnected birth and death processes. J. Appl. Prob. 5, 334–349.Google Scholar
Severo, N. C. (1967) Two theorems on solutions of differential-difference equations and applications to epidemic theory. J. Appl. Prob. 4, 271–280.CrossRefGoogle Scholar
Severo, N. C. (1969) A recursion theorem on solving differential-difference equations and applications to some stochastic processes. J. Appl. Prob. 6, 673–681.CrossRefGoogle Scholar
Severo, N. C. (1969) Generalizations of some stochastic epidemic models. Math. Biosci. 4, 395–402.Google Scholar
Severo, N. C. (1969) Right-shift processes. Proc. Nat. Acad. Sci. USA 64, 1162–1164.Google Scholar
Severo, N. C. (1969) The probabilities of some epidemie models. Biometrika 56, 197–201.Google Scholar
Severo, N. C. (1971) Multidimensional right-shift processes. Adv. Appl. Prob. 3, 200–201.Google Scholar