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Approaching in distribution with applications to resampling of stochastic processes
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Moscow state university.
2000 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 27, no 2, 371-384 p.Article in journal (Refereed) Published
Abstract [en]

We introduce the notion of weak approaching and conditionally weak approaching sequences of random processes. This notion generalizes the conventional weak convergence, and has been proposed for real valued random variables in Belyaev (1995). Some of the standard tools for an investigation of the behaviour of weak approaching sequences of random elements in metric spaces are developed. The spaces of smoothed and right-continuous functions with left-hand limits are considered. This technique allows us to use the resampling approach for an evaluation of distributions of continuous functionals on realizations of sum of an increasing number of independent random processes. Two numerical examples are presented for such functionals as supremum and number of level crossings.

Place, publisher, year, edition, pages
Wiley-VCH Verlagsgesellschaft, 2000. Vol. 27, no 2, 371-384 p.
Keyword [en]
extreme values; Gaussian processes; level crossings; resampling; weak approaching
National Category
Probability Theory and Statistics
URN: urn:nbn:se:umu:diva-87443DOI: 10.1111/1467-9469.00195ISI: 000087746000010OAI: diva2:709342
Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2014-04-16Bibliographically approved

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Belyaev, Yuri KSeleznjev, Oleg
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