Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60J10 Markov chains with discrete parameter
- 60K99 None of the above but in this section
- 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
- 60J45 Probabilistic potential theory, See also {31Cxx, 31D05}

**Résumé:** In this work we give a necessary and sufficient condition of recurrence for
correlated random walks on $\Z$. We consider also the case of an
i.i.d. environment,
compute their asymptotic velocity of escape to infinity, and notice a
"slowdown"
phenomena. For the continuous time counterpart of these walks on
$\R$, we give an analog
condition. In the transient case, the potential operator makes a
striking link with
diffusion processes.

**Mots Clés:** *Correlated random walks ; random environment ; potential operator*

**Date:** 2002-09-10

**Prépublication numéro:** *PMA-754*

**Pdf file : **PMA-754.pdf