On the recurrence set of planar Markov Random Walks

Loïc Hervé (1) , Françoise Pene (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LM - Laboratoire de mathématiques de Brest

In this paper, we investigate the properties of recurrent planar Markov random walks. More precisely, we study the set of recurrent points with the use of local limit theorems. The Nagaev-Guivarc'h spectral method provides several examples for which these local limit theorems are satisfied as soon as the (standard or non-standard) central limit theorem holds.

Mots clés: Recurrence; Markov chain; Spectral method

Domaines: Probabilités [math.PR]

Loïc Hervé, Françoise Pene. On the recurrence set of planar Markov Random Walks. Journal of Theoretical Probability, 2013, 26 (1), pp.169-197. ⟨10.1007/s10959-012-0414-7⟩. ⟨hal-00522041v2⟩