Electronic Communications in Probability

On recurrence of the multidimensional Lindley process

Wojciech Cygan and Judith Kloas

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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.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 4, 14 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks 60K25: Queueing theory [See also 68M20, 90B22] 60G52: Stable processes

ladder epoch Lindley process local contractivity random walk stable process

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Cygan, Wojciech; Kloas, Judith. On recurrence of the multidimensional Lindley process. Electron. Commun. Probab. 23 (2018), paper no. 4, 14 pp. doi:10.1214/18-ECP106. https://projecteuclid.org/euclid.ecp/1518426010

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