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 Singular integrals of stable subordinator Xu, Lihu1,2 2018-08 Source Publication STATISTICS & PROBABILITY LETTERS ISSN 0167-7152 Volume 139Pages: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. Keyword Alpha-stable Subordinator Singular Integral Of Alpha-stable Subordinator DOI https://doi.org/10.1016/j.spl.2018.04.008 URL View the original Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Statistics & Probability WOS ID WOS:000435046800015 Publisher ELSEVIER SCIENCE BV The Source to Article WOS Fulltext Access Citation statistics Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Corresponding Author Xu, Lihu Affiliation 1.Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macau2.UM Zhuhai Research Institute, Zhuhai, China First Author Affilication Faculty of Science and Technology Corresponding Author Affilication Faculty of Science and Technology Recommended CitationGB/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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