Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

How vertex reinforced jump process arises naturally

Xiaolin Zeng

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Abstract

We prove that the only nearest neighbor jump process with local dependence on the occupation times satisfying the partially exchangeable property is the vertex reinforced jump process, under some technical conditions (Theorem 4). This result gives a counterpart to the characterization of edge reinforced random walk given by Rolles (Probab. Theory Related Fields 126 (2003) 243–260).

Résumé

Nous montrons que le seul processus de saut sur les plus proches voisins avec une dépendance locale par rapport aux temps d’occupation et satisfaisant la propriété d’échangeabilité partielle est, sous quelques conditions techniques, le processus de saut avec renforcement par sommet (Théorème 4). Ce résultat donne une contrepartie à la caractérisation de la marche aléatoire avec renforcement par arête obtenue par Rolles (Probab. Theory Related Fields 126 (2003) 243–260).

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 52, Number 3 (2016), 1061-1075.

Dates
Received: 22 December 2013
Revised: 16 October 2014
Accepted: 8 February 2015
First available in Project Euclid: 28 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1469723511

Digital Object Identifier
doi:10.1214/15-AIHP671

Mathematical Reviews number (MathSciNet)
MR3531700

Zentralblatt MATH identifier
1350.60089

Subjects
Primary: 60G

Keywords
Partial exchangeability Vertex reinforced jump processes

Citation

Zeng, Xiaolin. How vertex reinforced jump process arises naturally. Ann. Inst. H. Poincaré Probab. Statist. 52 (2016), no. 3, 1061--1075. doi:10.1214/15-AIHP671. https://projecteuclid.org/euclid.aihp/1469723511


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