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Singular integrals of stable subordinator
Xu, Lihu1,2
2018-08
Source PublicationSTATISTICS & PROBABILITY LETTERS
ISSN0167-7152
Volume139Pages:115-118
Abstract

It is well known that f(0)(1) t(-theta)dt < infinity fore is an element of (0, 1) and f(0)(1) recit = infinity for theta is an element of [1, 00). Since t can be taken as an alpha-stable subordinator with alpha = 1, it is natural to ask whether f(0)(1); t(-theta)dS(t) has a similar property when S-t is an alpha-stable subordinator with a E (0, 1). We show that theta = 1/alpha is the border line such that integral(1)(0)t(-theta)dSt is finite a.s. for theta is an element of (0, 1/alpha) and blows up a.s. for theta is an element of [1/alpha, infinity). When alpha = 1, our result recovers that of f(0)(1)t(-theta) dt. Moreover, we give a pth moment estimate for the integral when theta is an element of (0, 1/alpha) (C) 2018 Elsevier B.V. All rights reserved.

KeywordAlpha-stable Subordinator Singular Integral Of Alpha-stable Subordinator
DOIhttps://doi.org/10.1016/j.spl.2018.04.008
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000435046800015
PublisherELSEVIER SCIENCE BV
The Source to ArticleWOS
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Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorXu, Lihu
Affiliation1.Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau
2.UM Zhuhai Research Institute, Zhuhai, China
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Xu, Lihu. Singular integrals of stable subordinator[J]. STATISTICS & PROBABILITY LETTERS,2018,139:115-118.
APA Xu, Lihu.(2018).Singular integrals of stable subordinator.STATISTICS & PROBABILITY LETTERS,139,115-118.
MLA Xu, Lihu."Singular integrals of stable subordinator".STATISTICS & PROBABILITY LETTERS 139(2018):115-118.
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