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2014 On functional weak convergence for partial sum processes
Danijel Krizmanic
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Electron. Commun. Probab. 19: 1-12 (2014). DOI: 10.1214/ECP.v19-3686

Abstract

For a strictly stationary sequence of regularly varying random variables we study functional weak convergence of partial sum processes in the space $D[0,1]$ with the $J_{1}$ topology. Under the strong mixing condition, we identify necessary and sufficient conditions for such convergence in terms of the corresponding extremal index. We also give conditions under which the regular variation property is a necessary condition for this functional convergence in the case of weak dependence.

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Danijel Krizmanic. "On functional weak convergence for partial sum processes." Electron. Commun. Probab. 19 1 - 12, 2014. https://doi.org/10.1214/ECP.v19-3686

Information

Accepted: 26 August 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1317.60031
MathSciNet: MR3254739
Digital Object Identifier: 10.1214/ECP.v19-3686

Subjects:
Primary: 60F17
Secondary: 60G52, 60G70

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