On recurrence of the multidimensional Lindley process

Wojciech Cygan; Judith Kloas

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arXiv · 1707.01714

On recurrence of the multidimensional Lindley process

Wojciech Cygan·Judith Kloas

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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.

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BibTeX RIS

Wojciech Cygan, Judith Kloas. 2017-07-06. On recurrence of the multidimensional Lindley process. https://arxiv.org/abs/1707.01714

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