Characterization of the inverse stable subordinator

Farouk Mselmi

Statistics & Probability Letters, 2018, vol. 140, issue C, 37-43

Abstract: In this paper, we characterize the class of the inverse stable subordinator (E(t))t>0 by an independence property with a positive random variable T. Moreover, we extend this subordinator to a bivariate stochastic process ((E1(t),E2(t)))t>0 and we establish a characterization of this process using the notion of cut in natural exponential family and some independence conditions. This allows us to show that this extended process comes from a mixture between a β-stable process, with β∈(0,2] and an inverse α-stable subordinator, with α∈(0,1). We consider separately the case β=1 and the case β≠1.

Keywords: Inverse stable subordinator; Natural exponential family; Stable processes (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.04.007

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