On a recursive solution for an \(n\)-dimensional Markov chain in continuous time. (Spanish. English summary) Zbl 0734.60077

Summary: A recursive solution for an n-dimensional Markov chain in continuous time, based on an integer function K, is considered. A work on the family of polynomials which arise in that solution is presented, in order to get the subfamily of polynomials that appears explicitly in the recursive solution, in terms of the absolute probability distribution, and the subfamily that is necessary and sufficient to compute in the recursive procedure, which brings about a substantial advantage in the automatic processing of such solution. This is carried out by the analysis of a class of subsets of Im(K). Moreover, a new expression for the solution is given.


60J27 Continuous-time Markov processes on discrete state spaces
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[1] BILLARD, L. (1981): “Generalized two-dimensional bounded birth and death processes and some applications{”.J. Appl., Prob., 18, 335–347.} · Zbl 0459.60074
[2] REQUENA, F. (1981): “Procedimiento de solución para una cadena de Markovn-dimensional de parámetro continuo{”.Cuadernos de Estadística Matemática, 6, 49–65.}
[3] REQUENA, F., y ORTEGA, L. (1985): “Sobre la solución de un modelo epidemiológico estocástico con inmunización{”. XV Reunión Nacional de Estadística e I. O., Gijón, 23 al 26 de septiembre.}
[4] REQUENA, F. (1986): “Estudio de una solución recursiva para una cadena de Markov en tiempo continuo, con aplicaciones epidemiológicas{”. XVI Reunión Nacional de Estadística e I. O., Málaga, 3 al 6 de noviembre.}
[5] SEVERO, N. C. (1969a): “A recursion theorem on solving differential-difference equations and applications to some stochastic processes{”.J. Appl. Prob., 6, 673–681.} · Zbl 0213.21901
[6] SEVERO, N. C. (1969b): “Right-Shift processes{”. Proc. Nat. Acad. Sci., U.S.A., 64, 1162–1164.} · Zbl 0206.19201
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