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On Subordinators, Self-Similar Markov Processes and Some Factorizations of the Exponential Variable

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	On Subordinators, Self-Similar Markov Processes and Some Factorizations of the Exponential Variable
2.	Creator	Author's name, affiliation, country	Jean Bertoin; Universite Pierre et Marie Curie
2.	Creator	Author's name, affiliation, country	Marc Yor; Universite Pierre et Marie Curie
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Self-similar Markov process, subordinator, exponential functional
3.	Subject	Subject classification	60J30.
4.	Description	Abstract	Let $\xi$ be a subordinator with Laplace exponent $\Phi$, $I=\int_{0}^{\infty}\exp(-\xi_s)ds$ the so-called exponential functional, and $X$ (respectively, $\hat X$) the self-similar Markov process obtained from $\xi$ (respectively, from $\hat{\xi}=-\xi$) by Lamperti's transformation. We establish the existence of a unique probability measure $\rho$ on $]0,\infty[$ with $k$-th moment given for every $k\in N$ by the product $\Phi(1)\cdots\Phi(k)$, and which bears some remarkable connections with the preceding variables. In particular we show that if $R$ is an independent random variable with law $\rho$ then $IR$ is a standard exponential variable, that the function $t\to E(1/X_t)$ coincides with the Laplace transform of $\rho$, and that $\rho$ is the $1$-invariant distribution of the sub-markovian process $\hat X$. A number of known factorizations of an exponential variable are shown to be of the preceding form $IR$ for various subordinators $\xi$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2001-11-05
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1039
10.	Identifier	Digital Object Identifier	10.1214/ECP.v6-1039
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 6
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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