Exact asymptotics and limit theorems for supremum of stationary -processes over a random interval

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• 作者：Zhongquan Tan^a ; Enkelejd Hashorva^b ; ^{Enkelejd.hashorva@unil.ch}
• 关键词：primary ; 60G15 ; secondary ; 60G70
• 刊名：Stochastic Processes and their Applications
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：123
• 期：8
• 页码：2983-2998
• 全文大小：252 K

文摘

Let be a stationary -process with degrees of freedom being independent of some non-negative random variable . In this paper we derive the exact asymptotics of as when has a regularly varying tail with index . Three other novel results of this contribution are the mixed Gumbel limit law of the normalised maximum over an increasing random interval, the Piterbarg inequality and the Seleznjev th-mean theorem for stationary -processes.