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On recurrence of the multidimensional Lindley process. (English) Zbl 1390.60167
Summary: 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.

MSC:
60G50 Sums of independent random variables; random walks
60K25 Queueing theory (aspects of probability theory)
60G52 Stable stochastic processes
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