期刊
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
卷 137, 期 5, 页码 1530-1543出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jspi.2006.09.003
关键词
finite birth-death processes; catastrophe processes; dual processes; transient probability functions; recursive; Cayley-Hamilton approach
A representation of the transient probability functions of finite birth-death processes (with or without catastrophes) as a linear combination of exponential functions is derived using a recursive, Cayley-Hamilton approach. This method of solution allows practitioners to solve for these transient probability functions by reducing the problem to three calculations: determining eigenvalues of the Q-matrix, raising the Q-matrix to an integer power and solving a system of linear equations. The approach avoids Laplace transforms and permits solution of a particular transition probability function from state i to j without determining all such functions. (c) 2006 Elsevier B.V. All rights reserved.
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