Markov chains with heavy-tailed increments and asymptotically zero drift

J. Lamperti, Criteria for the recurrence and transience of stochastic processes I, J. Math. Anal. Appl. 1

1960

Earlier work this paper cites.

J. Lamperti, A new class of probability limit theorems, J. Math. Mech. 11

1962

Earlier work this paper cites.

J. Lamperti, Criteria for stochastic processes. II. Passage-time moments, J. Math. Anal. Appl. 7

1963

Earlier work this paper cites.

B. A. Rogozin and S. G. Foss, The recurrence of an oscillating random walk, Theor. Probab. Appl. 23

1978

Earlier work this paper cites.

R. A. Doney, On the exact asymptotic behaviour of the distribution of ladder epochs, Stochastic Process. Appl. 12

1982

Earlier work this paper cites.

G. Fayolle, V. A. Malyshev and M. V. Menshikov, Topics in the Constructive Theory of Countable Markov Chains , Cambridge University Press, Cambridge, 1995

1995

Cited alongside, same era.

S. Aspandiiarov, R. Iasnogorodski and M. Menshikov, Passage-time moments for nonnegative stochastic processes and an application to reflected random walks in a quadrant, Ann. Probab. 24

1996

Cited alongside, same era.

O. Hryniv, I. M. MacPhee, M. V. Menshikov and A. R. Wade, Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips, Electron. J. Probab. 17

2012

Cited alongside, same era.

A. Gut, Probability: A Graduate Course , 2nd ed., Springer, New York, 2013

2013

Cited alongside, same era.

N. Sandrić, Recurrence and transience property for a class of Markov chains, Bernoulli , 19

2013

Cited alongside, same era.

D. Denisov, D. Korshunov and V. Wachtel, At the Edge of Criticality: Markov Chains with Asymptotically Zero Drift . arXiv:1612.01592

Original

Cited in the paper.

M. V. Menshikov, D. Petritis and A. R. Wade, Heavy-tailed random walks on complexes of half-lines, J. Theor. Probab. To appear. arXiv:1610.00881

Original

Cited in the paper.

N. Sandrić, Long-time behaviour of stable-like processes, Stochastic Process. Appl. 123

2013

Later among the works it cites.

N. Georgiou, M. V. Menshikov, A. Mijatović and A. R. Wade, Anomalous recurrence properties of many-dimensional zero-drift random walks, Adv. in Appl. Probab. 48A

2016

Later among the works it cites.

N. Sandrić, Ergodic property of stable-like Markov chains, J. Theor. Probab. 29

2016

Later among the works it cites.

M. Menshikov, S. Popov and A. Wade, Non-homogeneous Random Walks , Cambridge University Press, Cambridge, 2017

2017

Later among the works it cites.