Strong Gaussian approximation for cumulative processes with heavy tails

This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration periods and increments over them have only power moments of orde...

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Bibliographic Details
Published inarXiv.org
Main Authors Bashtova, Elena, Shashkin, Alexey
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.07.2020
Subjects
Approximation
Convergence
Gaussian process
Invariance
Mathematical analysis
Random processes
Regeneration
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Summary:This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration periods and increments over them have only power moments of order greater than 2. Under this power-type conditions two types of approximation by Wiener process are proved: the rate of convergence in the Strassen's invariance principle and inequalities for the probability that random process deviates from the approximating one.
ISSN:2331-8422