Criteria on ergodicity and strong ergodicity of single death processes

Abstract

Based on an explicit representation of moments of hitting times for single death processes, the criteria on ergodicity and strong ergodicity are obtained. These results can be applied for an extended class of branching processes. Meanwhile, some sufficient and necessary conditions for recurrence and exponential ergodicity as well as extinction probability for the processes are presented.

Keywords

Single death process / ergodicity / strong ergodicity / recurrence / moments of hitting times

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