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Existence and Uniqueness of Q ‐Processes with a Given Finite μ ‐Invariant Measure
Author(s) -
Pollett Phil,
Zhang Hanjun
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00317.x
Subject(s) - mathematics , uniqueness , countable set , invariant measure , invariant (physics) , measure (data warehouse) , pure mathematics , finite state , discrete mathematics , state space , combinatorics , mathematical analysis , mathematical physics , markov chain , statistics , database , computer science , ergodic theory
Summary Let Q be a stable and conservative Q ‐matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C . Suppose that Q admits a finite μ ‐subinvariant measure m on C . We derive necessary and sufficient conditions for there to exist a Q ‐process for which m is μ ‐invariant on C , as well as a necessary condition for the uniqueness of such a process.