Strong ergodicity of monotone transition functions

✍ Scribed by Hanjun Zhang; Anyue Chen; Xiang Lin; Zhenting Hou

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 90 KB
• Volume: 55
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00130-4

✦ Synopsis

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.