Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart (2024) Sample-Path Large Deviations for Unbounded Additive Functionals of the Reflected Random Walk. Mathematics of Operations Research 0(0). https://doi.org/10.1287/moor.2020.0094

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Abstract

We prove a sample-path large deviation principle (LDP) with sublinear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space D [0, 1] 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 Markov random walk, and we show that it exhibits a heavy-tailed behavior.

Authors
Mihail Bazhba, Jose Blanchet, Chang-Han Rhee, Bert Zwart
Publication date
2024/3/27
Journal
Mathematics of Operations Research
Publisher
INFORMS