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2018 On recurrence of the multidimensional Lindley process
Wojciech Cygan, Judith Kloas
Electron. Commun. Probab. 23: 1-14 (2018). DOI: 10.1214/18-ECP106

Abstract

A Lindley process arises from classical studies in queueing theory and it usually reflects waiting times of customers in single server models. In this note we study recurrence of its higher dimensional counterpart under some mild assumptions on the tail behaviour of the underlying random walk. There are several links between the Lindley process and the associated random walk and we build upon such relations. We apply a method related to discrete subordination for random walks on the integer lattice together with various facts from the theory of fluctuations of random walks.

Citation

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Wojciech Cygan. Judith Kloas. "On recurrence of the multidimensional Lindley process." Electron. Commun. Probab. 23 1 - 14, 2018. https://doi.org/10.1214/18-ECP106

Information

Received: 6 July 2017; Accepted: 2 January 2018; Published: 2018
First available in Project Euclid: 12 February 2018

zbMATH: 1390.60167
MathSciNet: MR3771762
Digital Object Identifier: 10.1214/18-ECP106

Subjects:
Primary: 60G50, 60G52, 60K25

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