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

2012/08/15 by Denis Denisov, Denisov, Denis, Dmitry Korshunov +3
Mathematics · #60F10 #60F15 #60J05 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60F10 #msc:60F15 #msc:60J05

paper · pdf · doi:10.48550/arxiv.1208.3066

27 pages

arxiv created 2012/08/15 · openalex publication_date 2012/08/15 · arxiv updated 2012/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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