Dwelling time for countable Markov chains. IV: Chains on an arbitrary tree (Q910103)

A Markov chain with a countable state space A and a transition function P is considered where (\(\forall a,b\in A)\) \(P(a,b)>0\Rightarrow P(b,a)>0\). The transition graph of the chain is assumed to be a tree (a connected non-oriented graph without any cycle). The Green function of this chain is constructed. Thus the author's results on a tree with a single branching knot proved in part III of this work [J. Sov. Math. 36, 451-461 (1987); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 142, 25-38 (1985; Zbl 0576.60066)] are generalized. Some suggestions are made for the occupation time field of the corresponding continuous time Markov process to be Markov.