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Functional limits of empirical distributions in crossing theory

Lindgren, Georg LU (1977) In Stochastic Processes and their Applications 5(2). p.143-149
Abstract
We present a functional limit theorem for the empirical level-crossing behaviour of a stationary Gaussian process. This leads to the well-known Slepian model process for a Gaussian process after an upcrossing of a prescribed level as a weak limit in C-space for an empirically defined finite set of functions.We also stress the importance of choosing a suitable topology by giving some natural examples of continuous and non-continuous functionals.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
functional limit theorem, empirical process, stationary normal process, level crossing
in
Stochastic Processes and their Applications
volume
5
issue
2
pages
143 - 149
publisher
Elsevier
external identifiers
  • scopus:0342510988
ISSN
1879-209X
language
English
LU publication?
yes
id
100eca99-21ff-44a2-abd7-c70a0ec4f979 (old id 1273155)
alternative location
http://ida.lub.lu.se/cgi-bin/elsevier_local?YMT00110-A-03044149-V0005I02-77900254
date added to LUP
2009-06-03 16:31:56
date last changed
2017-03-15 13:27:02
@article{100eca99-21ff-44a2-abd7-c70a0ec4f979,
  abstract     = {We present a functional limit theorem for the empirical level-crossing behaviour of a stationary Gaussian process. This leads to the well-known Slepian model process for a Gaussian process after an upcrossing of a prescribed level as a weak limit in C-space for an empirically defined finite set of functions.We also stress the importance of choosing a suitable topology by giving some natural examples of continuous and non-continuous functionals.},
  author       = {Lindgren, Georg},
  issn         = {1879-209X},
  keyword      = {functional limit theorem,empirical process,stationary normal process,level crossing},
  language     = {eng},
  number       = {2},
  pages        = {143--149},
  publisher    = {Elsevier},
  series       = {Stochastic Processes and their Applications},
  title        = {Functional limits of empirical distributions in crossing theory},
  volume       = {5},
  year         = {1977},
}