Existence and Uniqueness of Q‐Processes with a Given Finite μ‐Invariant Measure
Identifieur interne : 001E24 ( Main/Exploration ); précédent : 001E23; suivant : 001E25Existence and Uniqueness of Q‐Processes with a Given Finite μ‐Invariant Measure
Auteurs : Phil Pollett [Australie] ; Hanjun Zhang [Australie]Source :
- Australian & New Zealand Journal of Statistics [ 1369-1473 ] ; 2004-03.
English descriptors
Abstract
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.
Url:
DOI: 10.1111/j.1467-842X.2004.00317.x
Affiliations:
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<front><div type="abstract" xml:lang="en">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.</div>
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