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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

##### MSC:
 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60G50 Sums of independent random variables; random walks
##### Keywords:
local limit theorem; transient or recurrent