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, 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).
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).
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  2005 Feb 11 
Publisher  
ISBN (Print)  9162863843 
Publication status  Published  2005 
Bibliographical note
Defence detailsDate: 20050211
Time: 09:15
Place: Room A, MHbuilding, Lund Institute of Technology
External reviewer(s)
Name: Albin, Patrik
Title: Docent
Affiliation: Chalmers University of Technology

Subject classification (UKÄ)
 Probability Theory and Statistics
Free 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