Strong ergodicity of monotone transition functions
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.
Volume (Year): 55 (2001)
Issue (Month): 1 (November)
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