Asymptotic Expansions of Crossing Rates of Stationary Random Processes
Oskar Hagberg
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology
2005
ISBN 9162863843
LUTFMS10262005

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).





