On overload in a storage model, with a self-similar and infinitely divisible input

• 成果类型: Article
• 署名作者: Albin, JMP; Samorodnitsky, G
• 署名单位: Chalmers University of Technology; Cornell University; Cornell University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000125
• 发表日期: 2004
• 页码: 820-844
• 关键词: alpha-stable processes; mixed moving averages; extremes

摘要

Let {X(t)}(tgreater than or equal to0) be a locally bounded and infinitely divisible stochastic process, with no Gaussian component, that is self-similar with index H > 0. Pick constants gamma > H and c > 0. Let nu be the Levy measure on R-[0,R-infinity) of X, and suppose that R(u) equivalent to nu({y epsilon R-[0,R-infinity) :sup(tgreater than or equal to0) y(t)1/(1 + ct(gamma)) > u}) is suitably heavy tailed as u --> infinity (e.g., subexponential with positive decrease). For the storage process Y(t) equivalent to sup(sgreater than or equal tot) (X(s)-X(t)-c(s-t)(gamma)), we show that P{sup(Sepsilon[0,t(u)]) Y(s) > u} similar to P{Y((t) over cap (u)) > u} as u --> infinity, when 0 less than or equal to (t) over cap (u) less than or equal to t (u) do not grow too fast with u [e.g., t(u) = o(u(1/gamma))].