Potential analysis for positive recurrent Markov chains with asymptotically zero drift: power-type asymptotics

DOI10.1016/j.spa.2013.04.011zbMath1294.60096arXiv1208.3066OpenAlexW2163430306MaRDI QIDQ2447699

Denis Denisov, Vitali Wachtel, Dmitrii Korshunov

Publication date: 28 April 2014

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3066

zbMATH Keywords

harmonic functionMarkov chainrenewal functioninvariant distributionLamperti problemasymptotically zero driftmartingale techniquetest (Lyapunov) functionconvergence to \(\varGamma\)-distributionnon-exponential change of measureregularly varying tail behaviour

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Strong limit theorems (60F15) Large deviations (60F10)

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Strong transience for one-dimensional Markov chains with asymptotically zero drifts, Tail asymptotics for delay in a half-loaded \(\mathrm{GI}/\mathrm{GI}/2\) queue with heavy-tailed job sizes, Renewal theory for transient Markov chains with asymptotically zero drift, Markov chains with heavy-tailed increments and asymptotically zero drift, Random walks in cones

Cites Work

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• Excursions and local limit theorems for Bessel-like random walks
• Moments for stationary Markov chains with asymptotically zero drift
• Markov chains and stochastic stability
• Criteria for the recurrence or transience of stochastic process. I
• Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains
• Random walk weakly attracted to a wall
• Quenched and annealed critical points in polymer pinning models
• Asymptotic growth of controlled Galton-Watson processes
• Stochastic difference equations and generalized gamma distributions
• Asymptotic \(\Gamma\)-distribution for stochastic difference equations
• Asymptotic behaviour of stationary distributions for countable Markov chains, with some applications
• Markov processes with asymptotically zero drifts
• Random walks in cones
• On the existence of a regularly varying majorant of an integrable monotone function
• Criteria for stochastic processes. II: Passage-time moments
• One-dimensional asymptotically homogeneous Markov chains: Cramér transform and large deviation probabilities
• On population-size-dependent branching processes
• On recurrence and transience of growth models