Limit theorems for monotone Markov processes
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.
Keywords and phrasesMarkov processes coupling monotone i.i.d. maps polynomial convergence rates
AMS (2000) subject classificationPrimary 60F05, 60J05
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