SAMPLE PATH LARGE DEVIATIONS FOR LEVY PROCESSES AND RANDOM WALKS WITH REGULARLY VARYING INCREMENTS

• 成果类型: Article
• 署名作者: Rhee, Chang-Han; Blanchet, Jose; Zwart, Bert
• 署名单位: Northwestern University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1319
• 发表日期: 2019
• 页码: 3551-3605
• 关键词: stochastic recurrence equations; extremal behavior; subexponentiality; maximum; queues

摘要

Let X be a Levy process with regularly varying Levy measure v. We obtain sample-path large deviations for scaled processes (X) over bar (n) (t) (sic) X (nt)/n and obtain a similar result for random walks with regularly varying increments. Our results yield detailed asymptotic estimates in scenarios where multiple big jumps in the increment are required to make a rare event happen; we illustrate this through detailed conditional limit theorems. In addition, we investigate connections with the classical large deviations framework. In that setting, we show that a weak large deviation principle (with logarithmic speed) holds, but a full large deviation principle does not hold.