Tohoku Mathematical Journal
2023
March
SECOND SERIES VOL. 75, NO. 1

Tohoku Math. J.
75 (2023), 57-66

Title IRREDUCIBILITY AND UNIQUENESS OF SYMMETRIC MEASURE FOR MARKOV PROCESSES

Author Ping He and Jiangang Ying

(Received October 8, 2021, revised November 2, 2021)
Abstract. In this paper various irreducibilities for Markov processes related to topologies and excessive measures are discussed and their relations are presented. We shall mainly prove that, while the fine irreducibility is sufficient for the symmetric measure (and stationary distribution) to be unique if exists, it is almost necessary, namely $X$ is $m$-irreducible if $m$ is the unique symmetric measure for $X$.

Mathematics Subject Classification. Primary 60J40; Secondary 60J45.
Key words and phrases. Irreducibility, fine topology, excessive measures.

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