Abstract
This article considers the convergence to steady states of Markov processes generated by the action of successive i.i.d. monotone maps on a subset S of an Eucledian space. Without requiring irreducibility or Harris recurrence, a “splitting” condition guarantees the existence of a unique invariant probability as well as an exponential rate of convergence to it in an appropriate metric. For a special class of Harris recurrent processes on [0,∞) of interest in economics, environmental studies and queuing theory, criteria are derived for polynomial and exponential rates of convergence to equilibrium in total variation distance. Central limit theorems follow as consequences.
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Bhattacharya, R., Majumdar, M. & Hashimzade, N. Limit theorems for monotone Markov processes. Sankhya 72, 170–190 (2010). https://doi.org/10.1007/s13171-010-0005-6
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DOI: https://doi.org/10.1007/s13171-010-0005-6