Skip to Main content Skip to Navigation
Reports

Algebraic generating functions for two-dimensional random walks

Abstract : In this paper, we caracterize the solutions of specific bi-variate functional equations. The unknown functions represent the steady state distribution of specific two-dimensional random walks on Z2+. Inside the quarter plane, the jump have amplitude one, but are arbitrary on the axes. The main result is a necessary and sufficient condition for the solutions to be algebraic, when the "group" of the random walk (associated to an algebraic curve Q(x,y) = 0 having genus one) is finite. The method is based on Hilbert's factorization theorems, together with a uniformisation by means of elliptic functions.
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00075374
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 6:05:22 PM
Last modification on : Thursday, February 11, 2021 - 2:50:07 PM
Long-term archiving on: : Tuesday, April 12, 2011 - 10:48:14 PM

Identifiers

  • HAL Id : inria-00075374, version 1

Collections

Citation

Guy Fayolle, Roudolph Iasnogorodski, Vadim A. Malyshev. Algebraic generating functions for two-dimensional random walks. RR-1184, INRIA. 1990. ⟨inria-00075374⟩

Share

Metrics

Record views

196

Files downloads

76