Conditions for some non stationary random walks in the quarter plane to be singular or of genus 0 - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Markov Processes And Related Fields Année : 2021

Conditions for some non stationary random walks in the quarter plane to be singular or of genus 0

Résumé

We analyze the kernel K(x,y,t) of the basic functional equation associated with the tri-variate counting generating function (CGF) of walks in the quarter plane. In this short paper, taking t ∈]0, 1[, we provide the conditions on the jump probabilities {pi,j ’s} to decide whether walks are singular or regular, as defined in [3, Section 2.3]. These conditions are independent of t ∈]0, 1[ and given in terms of step set configurations. We also find the configurations for the kernel to be of genus 0, knowing that the genus is always ≤1. All these conditions are very similar to that of the stationary case considered in [3]. Our results extend the work [2], which considers only the special situation where t ∈]0, 1[ is a transcendental number over the field Q(pi,j). In addition, when p(0,0) = 0, our classification holds for all t ∈]0, +∞].
Fichier principal
Vignette du fichier
noyau.pdf (328.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03008556 , version 1 (16-11-2020)
hal-03008556 , version 2 (19-11-2020)
hal-03008556 , version 3 (10-01-2021)

Identifiants

  • HAL Id : hal-03008556 , version 3

Citer

Guy Fayolle, Roudolf Iasnogorodski. Conditions for some non stationary random walks in the quarter plane to be singular or of genus 0. Markov Processes And Related Fields, 2021, 27 (1), pp.12. ⟨hal-03008556v3⟩
153 Consultations
84 Téléchargements

Partager

Gmail Facebook X LinkedIn More