Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 4, Pages 724–743 (Mi smj2567)  
Blackwell-type theorems for weighted renewal functions

A. A. Borovkovab, K. A. Borovkovc

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c The University of Melbourne, Parkville, Australia
Full-text PDF (377 kB)
References:
PDF
HTML
Abstract: We establish Blackwell-type theorems for weighted renewal functions under much weaker conditions, as compared to the available, on the weight sequence and the distributions of the jumps in the renewal process. The proofs are based on using integro-local limit theorems and large deviation bounds. For the jump distribution, we consider conditions of the four types: (a) it has finite second moment, (b) it belongs to the domain of attraction of a stable law, (c) its tails are locally regularly varying, and (d) it satisfies the moment Cramér condition. In cases (a)–(c), the weights are assumed to satisfy a broad regularity condition on their moving averages, whereas in case (d) the weights can change exponentially fast.
Keywords: weighted renewal function, Blackwell theorem, integro-local limit theorems, Stone–Shepp theorems, large deviation probabilities, locally constant functions, regular variation.
Received: 07.02.2014
English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 4, Pages 589–605
DOI: https://doi.org/10.1134/S0037446614040028
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: A. A. Borovkov, K. A. Borovkov, “Blackwell-type theorems for weighted renewal functions”, Sibirsk. Mat. Zh., 55:4 (2014), 724–743; Siberian Math. J., 55:4 (2014), 589–605
Citation in format AMSBIB
\Bibitem{BorBor14}
\by A.~A.~Borovkov, K.~A.~Borovkov
\paper Blackwell-type theorems for weighted renewal functions
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 4
\pages 724--743
\mathnet{http://mi.mathnet.ru/smj2567}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3242591}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 4
\pages 589--605
\crossref{https://doi.org/10.1134/S0037446614040028}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000340941400002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906513896}
Linking options:
  • https://www.mathnet.ru/eng/smj2567
  • https://www.mathnet.ru/eng/smj/v55/i4/p724
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024