Sample-path large deviations for unbounded additive functionals of the reflected random walk

2020/03/31 by Bazhba, Mihail, Blanchet, Jose, Rhee, Chang-Han +1 · 1 citation
#60F10 (Primary) #60G17 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2003.14381

Abstract

We prove a sample path large deviation principle (LDP) with sub-linear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space \mathbbD[0,T] equipped with the M₁' topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area under the busy period of the MRW, and we show that it exhibits a heavy-tailed behavior.

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