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• W2847429107 abstract "We study the ergodic behaviour of a discrete-time $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $ttoinfty$. Convergence speed is estimated and an ergodic theorem is established for functionals of $X$. Our hypotheses on $X$ combine the standard small set and drift conditions for geometrically ergodic Markov chains with conditions on the growth rate of a certain maximal process of the random environment. We are able to cover a wide range of models that have heretofore been untractable. In particular, our results are pertinent to difference equations modulated by a stationary Gaussian process. Such equations arise in applications, for example, in discretized stochastic volatility models of mathematical finance." @default.
• W2847429107 created "2018-07-19" @default.
• W2847429107 creator A5060910753 @default.
• W2847429107 creator A5087944053 @default.
• W2847429107 date "2018-07-10" @default.
• W2847429107 modified "2023-09-27" @default.
• W2847429107 title "On the ergodicity of certain Markov chains in random environments." @default.
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• W2847429107 hasPublicationYear "2018" @default.
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