Subexponential asymptotics of hybrid fluid and ruin models

• 成果类型: Article
• 署名作者: Zwart, B; Borst, S; Debicki, K
• 署名单位: Eindhoven University of Technology; Centrum Wiskunde & Informatica (CWI); University of Wroclaw
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000648
• 发表日期: 2005
• 页码: 500-517
• 关键词: reduced load equivalence; gaussian-processes; queues; distributions; probabilities; supremum; FLOWS

摘要

We investigate the tail asymptotics of the supremum of X(t) + Y(t) - ct, where X = {X(t), t greater than or equal to 0} and Y = {Y(t), t greater than or equal to 0} are two independent stochastic processes. We assume that the process Y has subexponential characteristics and that the process X is more regular in a certain sense than Y. A key issue examined in earlier studies is under what conditions the process X contributes to large values of the supremum only through its average behavior. The present paper studies various scenarios where the latter is not the case, and the process X shows some form of atypical behavior as well. In particular, we consider a fluid model fed by a Gaussian process X and an (integrated) On-Off process Y. We show that, depending on the model parameters, the Gaussian process may contribute to the tail asymptotics by its moderate deviations, large deviations, or oscillatory behavior.