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Application d’un théorème limite local à la transience et à la recurrence de marches de Markov. (French) Zbl 0562.60074
Théorie du potentiel, Proc. Colloq. J. Deny, Orsay/France 1983, Lect. Notes Math. 1096, 301-332 (1984).
[For the entire collection see Zbl 0543.00004.]
In this paper the author considers a special type of Markov chains with state space \(X\times Z^ d\), these chains are invariant under translation. First of all, the author establishes a local limit theorem by using Fourier transformations and spectral theory, and then he proves that under some conditions, the chain is transient or recurrent according to \(d>2\) or \(d\leq 2\).
Reviewer: D.Hu

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60G50 Sums of independent random variables; random walks