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Singular integrals of stable subordinator

Lihu Xu

Statistics & Probability Letters, 2018, vol. 139, issue C, 115-118

Abstract: It is well known that ∫01t−θdt<∞ for θ∈(0,1) and ∫01t−θdt=∞ for θ∈[1,∞). Since t can be taken as an α-stable subordinator with α=1, it is natural to ask whether ∫01t−θdSt has a similar property when St is an α-stable subordinator with α∈(0,1). We show that θ=1α is the border line such that ∫01t−θdSt is finite a.s. for θ∈(0,1α) and blows up a.s. for θ∈[1α,∞). When α=1, our result recovers that of ∫01t−θdt. Moreover, we give a pth moment estimate for the integral when θ∈(0,1α).

Keywords: α-stable subordinator; Singular integral of α-stable subordinator (search for similar items in EconPapers)
Date: 2018
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