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

Mihail Bazhba; Jose Blanchet; Chang-Han Rhee; Bert Zwart

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arXiv · 2003.14381

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

Mihail Bazhba·Jose Blanchet·Chang-Han Rhee·Bert Zwart

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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 $\mathbb{D}[0,T]$ equipped with the $M_1'$ 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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BibTeX RIS

Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart. 2020-03-31. Sample-path large deviations for unbounded additive functionals of the reflected random walk. https://arxiv.org/abs/2003.14381

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