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Asymptotic Expansions of Crossing Rates of Stationary Random Processes

Hagberg, Oskar LU (2005)
Abstract (Swedish)
Popular Abstract in Swedish

Korsningsintensiteten for en stationär stokastisk process är ett värdefullt verktyg när man studerar fördelningen för våghöjder och för maxima av havsnivån. Denna avhandling betraktar två approximationstekniker för fall då korsningsintensiteten inte kan ges exakt.Båda tekniker använder en asymptotisk expansion, och första och andra ordningens termer i denna approximation ges explicit.



Paper A beskriver hur korsningsintensiteten används för att studera våghöjder och maxima av havsnivån och tjänar som en motivering för följande tre Papers. Paper B och C behandlar en approximationsteknik som föreslagits av Breitung (1988); Paper B betraktar specialfallet av en kvadratisk form av... (More)
Popular Abstract in Swedish

Korsningsintensiteten for en stationär stokastisk process är ett värdefullt verktyg när man studerar fördelningen för våghöjder och för maxima av havsnivån. Denna avhandling betraktar två approximationstekniker för fall då korsningsintensiteten inte kan ges exakt.Båda tekniker använder en asymptotisk expansion, och första och andra ordningens termer i denna approximation ges explicit.



Paper A beskriver hur korsningsintensiteten används för att studera våghöjder och maxima av havsnivån och tjänar som en motivering för följande tre Papers. Paper B och C behandlar en approximationsteknik som föreslagits av Breitung (1988); Paper B betraktar specialfallet av en kvadratisk form av en Gaussisk process medan Paper C betraktar det allmänna fall Breitung studerade. Paper D behandlar den så kallade sadelpunktapproximation av korsningsintensiteten, någonting som tidigare studerats av Butler et al (2003). (Less)
Abstract
The crossing rate of a stationary random process is a valuble tool when studying crest hight distributions and maxima of sea level elevation. This thesis considers two approximation techinques for cases when the crossing rate cannot be exactly computed. Both techniques use an asymptotic expansion, and the first and second order terms in these expansions are given explicitly.



Paper A describes how the rate of crossings is used to study crest hight distributions and maxima of sea level elevation and serves as a motivation for the subsequent three papers. Paper B and C both study an approximation technique proposed by Breitung (1988); Paper B considers the special case of the quadratic form of a Gaussian random process,... (More)
The crossing rate of a stationary random process is a valuble tool when studying crest hight distributions and maxima of sea level elevation. This thesis considers two approximation techinques for cases when the crossing rate cannot be exactly computed. Both techniques use an asymptotic expansion, and the first and second order terms in these expansions are given explicitly.



Paper A describes how the rate of crossings is used to study crest hight distributions and maxima of sea level elevation and serves as a motivation for the subsequent three papers. Paper B and C both study an approximation technique proposed by Breitung (1988); Paper B considers the special case of the quadratic form of a Gaussian random process, while Paper C considers the general case that Breitung studied. Papers D treats the so- called Saddle point approximation of the crossing rate, allready studied informally by Butler et al (2003). (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Docent Albin, Patrik, Chalmers University of Technology
organization
publishing date
type
Thesis
publication status
published
subject
keywords
actuarial mathematics, Statistik, operationsanalys, aktuariematematik, programming, operations research, Matematik, Statistics, sea elevation, Mathematics, asymptotic expansions, wave crest hight distribution, Saddle point approximations, Crossing rate, programmering
pages
137 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Room A, MH-building, Lund Institute of Technology
defense date
2005-02-11 09:15
ISSN
1404-0034
ISBN
91-628-6384-3
language
English
LU publication?
yes
id
12d0c93c-2bdf-463f-a531-1321cd69ee5f (old id 544266)
date added to LUP
2007-09-27 15:41:51
date last changed
2016-09-19 08:44:53
@phdthesis{12d0c93c-2bdf-463f-a531-1321cd69ee5f,
  abstract     = {The crossing rate of a stationary random process is a valuble tool when studying crest hight distributions and maxima of sea level elevation. This thesis considers two approximation techinques for cases when the crossing rate cannot be exactly computed. Both techniques use an asymptotic expansion, and the first and second order terms in these expansions are given explicitly.<br/><br>
<br/><br>
Paper A describes how the rate of crossings is used to study crest hight distributions and maxima of sea level elevation and serves as a motivation for the subsequent three papers. Paper B and C both study an approximation technique proposed by Breitung (1988); Paper B considers the special case of the quadratic form of a Gaussian random process, while Paper C considers the general case that Breitung studied. Papers D treats the so- called Saddle point approximation of the crossing rate, allready studied informally by Butler et al (2003).},
  author       = {Hagberg, Oskar},
  isbn         = {91-628-6384-3},
  issn         = {1404-0034},
  keyword      = {actuarial mathematics,Statistik,operationsanalys,aktuariematematik,programming,operations research,Matematik,Statistics,sea elevation,Mathematics,asymptotic expansions,wave crest hight distribution,Saddle point approximations,Crossing rate,programmering},
  language     = {eng},
  pages        = {137},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  title        = {Asymptotic Expansions of Crossing Rates of Stationary Random Processes},
  year         = {2005},
}