Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7547952 | Statistics & Probability Letters | 2018 | 7 Pages |
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 βâ(0,2]
and an inverse α-stable subordinator, with αâ(0,1). We consider separately the case β=1
and the case βâ 1.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Farouk Mselmi,