State-dependent criteria for convergence of Markov chains (Q1327609)

By using state-dependent step mean drift (and random-step) conditions, criteria for Harris recurrence, positive recurrence and geometric ergodicity are obtained for time-discrete Markov chains on general state spaces. This extends the classical Foster-Lyapunov approach for denumerable Markov chains [see the authors, Markov chains and stochastic stability (Springer, 1993) and \textit{V. A. Malyshev} and \textit{M. V. Men'shikov}, Trans. Mosc. Math. Soc. 1981, No. 1, 1-48 (1981); translation from Tr. Mosk. Mat. O.-va 39, 3-48 (1979; Zbl 0441.60073)]. Applications to antibody activity, to nonlinear threshold autoregression and to complex queueing models are provided.