期刊
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
卷 52, 期 4, 页码 973-987出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2021.1921806
关键词
Cauchy's integral formula; embedding problem; manpower planning; Markov chains; stochastic matrices
This article discusses an important issue in manpower planning, which is obtaining a transition matrix over a short time interval using only a transition matrix over a longer time interval. The article derives a new representation for embeddable stochastic matrices by using Cauchy's integral formula and provides new conditions for embeddability and regularization.
In manpower planning there is an interesting, practically important and open challenging issue arising from the instances where a transition matrix over a certain short time interval is required but only a transition matrix over a longer time interval may be available. For example, the problem of finding a meaningful p-th root of an observable stochastic matrix within the context of Markov chains. The more general problem is divided into three phases, viz. embeddability, inverse, and identification problems. By exploiting the Cauchy's integral formula with the integrand defined on the Runnenberg's heart-shaped region, a new representation for a stochastic matrix that is embeddable is derived. New conditions for embeddability and regularization of stochastic matrices are provided. Examples are presented to illustrate the utility of the Cauchy's representation formula and its consequences.
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