Random walks in Z_+^2 with non-zero drift absorbed at the axes

Irina Kurkova (1) , Kilian Raschel (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Spatially homogeneous random walks in Z_+^2 with non-zero jump probabilities at distance at most 1, with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.

Mots clés: Random walk; Green functions; Absorption probabilities; Singularities of complex functions; Holomorphic continuation; Steepest descent method.; Steepest descent method

Domaines: Probabilités [math.PR]

Irina Kurkova, Kilian Raschel. Random walks in Z_+^2 with non-zero drift absorbed at the axes. Bulletin de la société mathématique de France, 2011, 139 (3), pp.287-295. ⟨hal-00372260⟩