Tail behaviour of stationary distribution for Markov chains with asymptotically zero drift

Denis Denisov; Dmitry Korshunov; Vitali Wachtel

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arXiv · 1208.3066

Tail behaviour of stationary distribution for Markov chains with asymptotically zero drift

Denis Denisov·Dmitry Korshunov·Vitali Wachtel

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Abstract

We consider a Markov chain on $R^+$ with asymptotically zero drift and finite second moments of jumps which is positive recurrent. A power-like asymptotic behaviour of the invariant tail distribution is proven; such a heavy-tailed invariant measure happens even if the jumps of the chain are bounded. Our analysis is based on test functions technique and on construction of a harmonic function.

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Denis Denisov, Dmitry Korshunov, Vitali Wachtel. 2012-08-15. Tail behaviour of stationary distribution for Markov chains with asymptotically zero drift. https://arxiv.org/abs/1208.3066

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