Existence and uniqueness of Q-processes with a given finite μ-invariant measure
Pollett, P. and Zhang, H. J. (2004) Existence and uniqueness of Q-processes with a given finite μ-invariant measure. Australian & New Zealand Journal of Statistics, 461: 113-120. doi:10.1111/j.1467-842X.2004.00317.x
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 mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.