Unified representation of formulas for single birth processes

Abstract

Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.) for the processes are presented.

Keywords

Single birth process / Poisson equation / uniqueness / recurrence / ergodicity / moments of return time

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Higher Education Press and Springer-Verlag Berlin Heidelberg