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March 2015 Convergence to stable laws in the space D
François Roueff, Philippe Soulier
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J. Appl. Probab. 52(1): 1-17 (March 2015). DOI: 10.1239/jap/1429282603

Abstract

We study the convergence of centered and normalized sums of independent and identically distributed random elements of the space D of càdlàg functions endowed with Skorokhod's J1 topology, to stable distributions in D. Our results are based on the concept of regular variation on metric spaces and on point process convergence. We provide some applications; in particular, to the empirical process of the renewal-reward process.

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François Roueff. Philippe Soulier. "Convergence to stable laws in the space D." J. Appl. Probab. 52 (1) 1 - 17, March 2015. https://doi.org/10.1239/jap/1429282603

Information

Published: March 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1326.60039
MathSciNet: MR3336843
Digital Object Identifier: 10.1239/jap/1429282603

Subjects:
Primary: 60G52
Secondary: 60G55, 60G70

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 1 • March 2015
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