On some transformations of bilateral birth-and-death processes with applications

Abstract

A method yielding simple relationships among bilateral birth-and-death processes is outlined. This allows one to relate birth and death rates of two processes in such a way that their transition probabilities, first-passage-time densities and ultimate crossing probabilities are mutually related by some product-form expressions.

4 pages; appeared in: The 17th Symposium of Information Theory and Its Applications (SITA '94), Hiroshima, Japan, December 6-9, 1994, pp. 739-742