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

Zhongquan Tan and Enkelejd Hashorva

Stochastic Processes and their Applications, 2013, vol. 123, issue 8, 2983-2998

Abstract: Let {χk(t),t≥0} be a stationary χ-process with k degrees of freedom being independent of some non-negative random variable T. In this paper we derive the exact asymptotics of P{supt∈[0,T]χk(t)>u} as u→∞ when T has a regularly varying tail with index λ∈[0,1). 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 pth-mean theorem for stationary χ-processes.

Keywords: χ-process; Limit theorems; Piterbarg inequality; Piterbarg theorem for χ-processes; Seleznjev pth-mean approximation theorem (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414913000732
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:8:p:2983-2998

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2013.03.009

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().