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Description
  • We study an extremal behavior of stochastic integrals with respect to Brownian motion. As the main result we obtain an exact tail behavior of a supremum of these integrals taken over [0,h] with h}0 fixed, and a limiting distribution of the supremum on intervals [0,T]. We show how the limit distribution is connected to an asymptotic of maximally selected quasi-likelihood procedure that is used to detect changes at an unknown time in polynomial regress on models. In an application to global near-surface temperatures we demonstrate that the limit results presented in the paper perform well for real data sets.
  • We study an extremal behavior of stochastic integrals with respect to Brownian motion. As the main result we obtain an exact tail behavior of a supremum of these integrals taken over [0,h] with h}0 fixed, and a limiting distribution of the supremum on intervals [0,T]. We show how the limit distribution is connected to an asymptotic of maximally selected quasi-likelihood procedure that is used to detect changes at an unknown time in polynomial regress on models. In an application to global near-surface temperatures we demonstrate that the limit results presented in the paper perform well for real data sets. (en)
Title
  • Extreme value theory for stochastic integrals of Legendre polynomials
  • Extreme value theory for stochastic integrals of Legendre polynomials (en)
skos:prefLabel
  • Extreme value theory for stochastic integrals of Legendre polynomials
  • Extreme value theory for stochastic integrals of Legendre polynomials (en)
skos:notation
  • RIV/00216208:11320/09:00206642!RIV10-GA0-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/06/0186), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 100
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 314499
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/09:00206642
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Extreme; value; theory; stochastic; integrals; Legendre; polynomials (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [5817A5BA6A5D]
http://linked.open...i/riv/nazevZdroje
  • Journal of Multivariate Analysis
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2009
http://linked.open...iv/tvurceVysledku
  • Aue, Alexander
  • Horvath, Lajos
  • Hušková, Marie
http://linked.open...ain/vavai/riv/wos
  • 000263983200016
http://linked.open...n/vavai/riv/zamer
issn
  • 0047-259X
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
is http://linked.open...avai/riv/vysledek of
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