Conditions for some non stationary random walks in the quarter plane to be singular or of genus 0 - Archive ouverte HAL Access content directly
Journal Articles Markov Processes And Related Fields Year : 2021

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

(1, 2) , (3)
1
2
3

Abstract

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
Origin : Files produced by the author(s)

Dates and versions

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

Identifiers

  • HAL Id : hal-03008556 , version 3

Cite

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⟩
129 View
76 Download

Share

Gmail Facebook Twitter LinkedIn More