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Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 2, Pages 387–396 (Mi tvp4512)  

This article is cited in 6 scientific papers (total in 6 papers)

Short Communications

A key renewal theorem for heavy tail distributions with $\beta\in(0,0.5]$

V. A. Vatutina, V. A. Topchiib

a Steklov Mathematical Institute of the Russian Academy of Sciences
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: An asymptotic behavior of increments of the renewal functions generated by the distributions with tails varying at $\pm\infty$ regularly with index $\beta\in(0,0.5]$ is investigated.

Keywords: increments of renewal function; infinite Mean; stable law on the real line; nonlattice distribution; regularly varying functions.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00515-a


DOI: https://doi.org/10.4213/tvp4512

Full text: PDF file (168 kB)
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English version:
Theory of Probability and its Applications, 2014, 58:2, 333–342

Bibliographic databases:

Document Type: Article
MSC: 60
Received: 29.02.2012

Citation: V. A. Vatutin, V. A. Topchii, “A key renewal theorem for heavy tail distributions with $\beta\in(0,0.5]$”, Teor. Veroyatnost. i Primenen., 58:2 (2013), 387–396; Theory Probab. Appl., 58:2 (2014), 333–342

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Valentin A. Topchiy, “Two-dimensional renewal theorems with weak moment conditions and critical Bellman – Harris branching processes”, Discrete Math. Appl., 26:1 (2016), 51–69  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Zh. Chi, “Strong renewal theorems with infinite mean beyond local large deviations”, Ann. Appl. Probab., 25:3 (2015), 1513–1539  crossref  mathscinet  zmath  isi
    3. Kevei P., “A note on the Kesten–Grincevičius–Goldie theorem”, Electron. Commun. Probab., 21 (2016), 51  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. A. Topchiǐ, “On renewal matrices connected with branching processes with tails of distributions of different orders”, Siberian Adv. Math., 28:2 (2018), 115–153  mathnet  crossref  crossref  elib
    5. V. A. Vatutin, V. A. Topchii, “Momenty mnogomernykh kriticheskikh protsessov Bellmana–Kharrisa s razlichnoi skorostyu ubyvaniya khvostov raspredelenii prodolzhitelnosti zhizni chastits”, Sib. elektron. matem. izv., 14 (2017), 1248–1264  mathnet  crossref
    6. Zh. Chi, “On a multivariate strong renewal theorem”, J. Theor. Probab., 31:3 (2018), 1235–1272  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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