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 Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 1, Pages 80–89 (Mi tvp2995)

On the asymptotics of the density of an infinitely divisible distribution at infinity

A. L. Yakymiv

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper the asymptotic properties at infinity of the density of an infinitely divisible distribution are studied in the case where an absolutely continuous component of the Lévy measure of this distribution varies dominantly at infinity. The presentation is given in terms of the so-called weak equivalence of functions which, in the case of weakly oscillating, and, in particular, the case of the density of an infinite divisible distribution regularly varying at infinity, coincides with ordinary equivalence.

Keywords: infinitely divisible distributions, spectral Lévy measure, density of a distribution, weak equivalence of functions, regularly varying functions, weakly oscillating functions, dominated variation of functions.

DOI: https://doi.org/10.4213/tvp2995

Full text: PDF file (813 kB)

English version:
Theory of Probability and its Applications, 2003, 47:1, 114–122

Bibliographic databases:

Citation: A. L. Yakymiv, “On the asymptotics of the density of an infinitely divisible distribution at infinity”, Teor. Veroyatnost. i Primenen., 47:1 (2002), 80–89; Theory Probab. Appl., 47:1 (2003), 114–122

Citation in format AMSBIB
\Bibitem{Yak02} \by A.~L.~Yakymiv \paper On the asymptotics of the density of an infinitely divisible distribution at infinity \jour Teor. Veroyatnost. i Primenen. \yr 2002 \vol 47 \issue 1 \pages 80--89 \mathnet{http://mi.mathnet.ru/tvp2995} \crossref{https://doi.org/10.4213/tvp2995} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1978697} \zmath{https://zbmath.org/?q=an:1033.60010} \transl \jour Theory Probab. Appl. \yr 2003 \vol 47 \issue 1 \pages 114--122 \crossref{https://doi.org/S0040585X97979469} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000183800400009} 

• http://mi.mathnet.ru/eng/tvp2995
• https://doi.org/10.4213/tvp2995
• http://mi.mathnet.ru/eng/tvp/v47/i1/p80

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Pakes A.G., “Convolution equivalence and infinite divisibility”, J. Appl. Probab., 41:2 (2004), 407–424
2. Kaleta K., Sztonyk P., “Spatial Asymptotics At Infinity For Heat Kernels of Integro-Differential Operators”, Trans. Am. Math. Soc., 371:9 (2019), 6627–6663
3. Barker A., “Transience and Recurrence of Markov Processes With Constrained Local Time”, ALEA-Latin Am. J. Probab. Math. Stat., 17:2 (2020), 993–1045
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