Further criteria for positive Harris recurrence of Markov chains (Q2701652)

The authors give several necessary and sufficient conditions for a Markov chain on a general state space \((X,\mathcal{B})\) to be positive Harris recurrent. These conditions involve only the asymptotic behavior of the sequence of expected occupation measures \(S^{(n)}(x, B):= n^{-1} \sum_{t=1}^n P^t(x,B)\), where \(P^t\) is the \(t\)-step transition kernel. The main result says that the chain is positive Harris recurrent if and only if for each \(B\in \mathcal{B}\) there exists \(a_B\geq 0\) such that \(S^{(n)}(x,B)\to a_B\) for each \(x\in X\).