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Strong ergodicity of monotone transition functions

Strong ergodicity of monotone transition functions

Zhang, Hanjun, Chen, Anyue, Lin, Xiang and Hou, Zhenting (2001) Strong ergodicity of monotone transition functions. Statistics & Probability Letters, 55 (1). pp. 63-69. ISSN 0167-7152 (doi:10.1016/S0167-7152(01)00130-4)

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Abstract

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

Item Type: Article
Uncontrolled Keywords: Feller minimal transition functions, monotone transition functions, Feller–Reuter–Riley transition functions, Feller–Reuter–Riley q-matrices, ordinary ergodicity, strong ergodicity, zero-entrance
Subjects: Q Science > QA Mathematics
Pre-2014 Departments: School of Computing & Mathematical Sciences
Related URLs:
Last Modified: 14 Oct 2016 09:00
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/567

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