Subgeometric Rates of Convergence of f-Ergodic Markov Chains
- 1 September 1994
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 26 (3) , 775-798
- https://doi.org/10.2307/1427820
Abstract
Let Φ = {Φ n} be an aperiodic, positive recurrent Markov chain on a general state space, π its invariant probability measure and f ≧ 1. We consider the rate of (uniform) convergence of Ex[g(Φ n)] to the stationary limit π (g) for |g| ≦ f: specifically, we find conditions under which as n →∞, for suitable subgeometric rate functions r. We give sufficient conditions for this convergence to hold in terms of(i) the existence of suitably regular sets, i.e. sets on which (f, r)-modulated hitting time moments are bounded, and(ii) the existence of (f, r)-modulated drift conditions (Foster–Lyapunov conditions).The results are illustrated for random walks and for more general state space models.Keywords
This publication has 13 references indexed in Scilit:
- Stability of Markovian processes I: criteria for discrete-time ChainsAdvances in Applied Probability, 1992
- Non-linear time series and Markov chainsAdvances in Applied Probability, 1990
- On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivalsJournal of Applied Probability, 1985
- The queue GI/G/1: Finite moments of the cycle variables and uniform rates of convergenceStochastic Processes and their Applications, 1985
- The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theoryStochastic Processes and their Applications, 1983
- The coupling of regenerative processesAdvances in Applied Probability, 1983
- The existence of moments for stationary Markov chainsJournal of Applied Probability, 1983
- Geometric ergodicity of Harris recurrent Marcov chains with applications to renewal theoryStochastic Processes and their Applications, 1982
- On coupling of discrete renewal processesProbability Theory and Related Fields, 1979
- Geometric Ergodicity and R-positivity for General Markov ChainsThe Annals of Probability, 1978