Extremes of Gaussian processes over an infinite horizon

A.B. Dieker

Stochastic Processes and their Applications, 2005, vol. 115, issue 2, 207-248

Abstract: Consider a centered separable Gaussian process Y with a variance function that is regularly varying at infinity with index 2H[set membership, variant](0,2). Let [phi] be a 'drift' function that is strictly increasing, regularly varying at infinity with index [beta]>H, and vanishing at the origin. Motivated by queueing and risk models, we investigate the asymptotics for u-->[infinity] of the probability P(supt[greater-or-equal, slanted]0Yt-[phi](t)>u) as u-->[infinity]. To obtain the asymptotics, we tailor the celebrated double sum method to our general framework. Two different families of correlation structures are studied, leading to four qualitatively different types of asymptotic behavior. A generalized Pickands' constant appears in one of these cases. Our results cover both processes with stationary increments (including Gaussian integrated processes) and self-similar processes.

Keywords: Extreme; values; Gaussian; processes; Ruin; probability; Regular; variation (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(04)00140-1
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:115:y:2005:i:2:p:207-248

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

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 ().