No Cover Image

Journal article 1171 views 210 downloads

Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues

Dmitri Finkelshtein Orcid Logo, Pasha Tkachov

Advances in Applied Probability, Volume: 50, Issue: 02, Pages: 373 - 395

Swansea University Author: Dmitri Finkelshtein Orcid Logo

Check full text

DOI (Published version): 10.1017/apr.2018.18

Abstract

We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times n. We prove Kesten's bound, which gives a uniform in n...

Full description

Published in: Advances in Applied Probability
ISSN: 0001-8678 1475-6064
Published: Applied Probability Trust/Cambridge University Press 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa38336
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2018-01-30T05:24:51Z
last_indexed 2021-02-24T03:58:28Z
id cronfa38336
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2021-02-23T14:03:27.3702808</datestamp><bib-version>v2</bib-version><id>38336</id><entry>2018-01-29</entry><title>Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues</title><swanseaauthors><author><sid>4dc251ebcd7a89a15b71c846cd0ddaaf</sid><ORCID>0000-0001-7136-9399</ORCID><firstname>Dmitri</firstname><surname>Finkelshtein</surname><name>Dmitri Finkelshtein</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2018-01-29</date><deptcode>SMA</deptcode><abstract>We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular sub-exponential functions and use it to find an analogue of Kesten's bound for functions on R^d. The results are applied for the study of the fundamental solution to a nonlocal heat-equation.</abstract><type>Journal Article</type><journal>Advances in Applied Probability</journal><volume>50</volume><journalNumber>02</journalNumber><paginationStart>373</paginationStart><paginationEnd>395</paginationEnd><publisher>Applied Probability Trust/Cambridge University Press</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0001-8678</issnPrint><issnElectronic>1475-6064</issnElectronic><keywords>sub-exponential densities; long-tail functions; heavy-tailed distributions; convolution tails; tail-equivalence; asymptotic behavior</keywords><publishedDay>30</publishedDay><publishedMonth>6</publishedMonth><publishedYear>2018</publishedYear><publishedDate>2018-06-30</publishedDate><doi>10.1017/apr.2018.18</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2021-02-23T14:03:27.3702808</lastEdited><Created>2018-01-29T22:47:56.3291613</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Dmitri</firstname><surname>Finkelshtein</surname><orcid>0000-0001-7136-9399</orcid><order>1</order></author><author><firstname>Pasha</firstname><surname>Tkachov</surname><order>2</order></author></authors><documents><document><filename>0038336-29012018225327.pdf</filename><originalFilename>FT-SubExp-AcceptedVersion.pdf</originalFilename><uploaded>2018-01-29T22:53:27.5370000</uploaded><type>Output</type><contentLength>481761</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-01-29T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2021-02-23T14:03:27.3702808 v2 38336 2018-01-29 Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues 4dc251ebcd7a89a15b71c846cd0ddaaf 0000-0001-7136-9399 Dmitri Finkelshtein Dmitri Finkelshtein true false 2018-01-29 SMA We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular sub-exponential functions and use it to find an analogue of Kesten's bound for functions on R^d. The results are applied for the study of the fundamental solution to a nonlocal heat-equation. Journal Article Advances in Applied Probability 50 02 373 395 Applied Probability Trust/Cambridge University Press 0001-8678 1475-6064 sub-exponential densities; long-tail functions; heavy-tailed distributions; convolution tails; tail-equivalence; asymptotic behavior 30 6 2018 2018-06-30 10.1017/apr.2018.18 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2021-02-23T14:03:27.3702808 2018-01-29T22:47:56.3291613 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Dmitri Finkelshtein 0000-0001-7136-9399 1 Pasha Tkachov 2 0038336-29012018225327.pdf FT-SubExp-AcceptedVersion.pdf 2018-01-29T22:53:27.5370000 Output 481761 application/pdf Accepted Manuscript true 2018-01-29T00:00:00.0000000 true eng
title Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
spellingShingle Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
Dmitri Finkelshtein
title_short Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
title_full Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
title_fullStr Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
title_full_unstemmed Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
title_sort Kesten's bound for subexponential densities on the real line and its multi-dimensional analogues
author_id_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf
author_id_fullname_str_mv 4dc251ebcd7a89a15b71c846cd0ddaaf_***_Dmitri Finkelshtein
author Dmitri Finkelshtein
author2 Dmitri Finkelshtein
Pasha Tkachov
format Journal article
container_title Advances in Applied Probability
container_volume 50
container_issue 02
container_start_page 373
publishDate 2018
institution Swansea University
issn 0001-8678
1475-6064
doi_str_mv 10.1017/apr.2018.18
publisher Applied Probability Trust/Cambridge University Press
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular sub-exponential functions and use it to find an analogue of Kesten's bound for functions on R^d. The results are applied for the study of the fundamental solution to a nonlocal heat-equation.
published_date 2018-06-30T03:48:29Z
_version_ 1763752342817079296
score 11.035634

Similar Items