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Pré-Publication, Document De Travail Année : 2016

The type problem for a class of inhomogeneous random walks : a series criterion by a probabilistic argument

Résumé

In the classical framework, a random walk on a group is a Markov chain with independent and identically distributed increments. In some sense, random walks are time and space homogeneous. In this paper, we are interested in a class of weakly inhomogeneous random walks termed Random Walk with Random Transition Probabilities — we refer to [18] for the terminology. As an application, we give a criterion for the recurrence or transience of these processes in the discrete Abelian case. This criterion is deduced using Fourier analysis of Markov additive processes and a perturbation argument of a Markov operator. The latter extends the results of the literature since it does not involve a quasi-compacity condition on the operator. Finally, we apply this criterion on some well known examples of random walks on directed graphs embedded in Z 2. Despite the type problem has been already solved for these examples, our analysis brought a new insight to this problematic.
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Dates et versions

hal-01274873 , version 1 (16-02-2016)
hal-01274873 , version 2 (12-05-2016)
hal-01274873 , version 3 (13-06-2016)
hal-01274873 , version 4 (18-01-2018)
hal-01274873 , version 5 (07-08-2020)
hal-01274873 , version 6 (22-06-2022)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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  • HAL Id : hal-01274873 , version 1

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Basile de Loynes. The type problem for a class of inhomogeneous random walks : a series criterion by a probabilistic argument. 2016. ⟨hal-01274873v1⟩
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