ON RECURRENCE OF REFLECTED RANDOM WALK ON THE HALF-LINE

Marc Peigné (1) , Wolfgang Woess (2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 TU Graz - Institut für Mathematische Strukturtheorie (Math C)

Abstract. Let (Yn) be a sequence of i.i.d. real valued random variables. Reflected random walk (Xn) is defined recursively by X0 = x ≥ 0, Xn+1 = |Xn − Yn+1|. In this note, we study recurrence of this process, extending a previous criterion. This is obtained by determining an invariant measure of the embedded process of reflections.

Domaines: Systèmes dynamiques [math.DS]

Marc Peigné, Wolfgang Woess. ON RECURRENCE OF REFLECTED RANDOM WALK ON THE HALF-LINE. 2006. ⟨hal-00360868⟩