Sample-Path Large Deviations for Unbounded Additive Functionals of the Reflected Random Walk

• 成果类型: Article
• 署名作者: Bazhba, Mihail; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert
• 署名单位: University of Amsterdam; Stanford University; Northwestern University; Eindhoven University of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.0094
• 发表日期: 2025
• 关键词: principles

摘要

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.