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The Self-Similar Dynamics of Renewal Processes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	The Self-Similar Dynamics of Renewal Processes
2.	Creator	Author's name, affiliation, country	Albert Meads Fisher; University of Sao Paulo; Brazil
2.	Creator	Author's name, affiliation, country	Marina Talet; Université de Provence; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	stable process, renewal process, Mittag-Leffler process, Cauchy process, almost-sure invariance principle in log density, pathwise Central Limit Theorem.
3.	Subject	Subject classification	Primary 37A50, 60F17, 60K05; secondary 60G18, 60G52.
4.	Description	Abstract	We prove an almost sure invariance principle in log density for renewal processes with gaps in the domain of attraction of an $\alpha$-stable law. There are three different types of behavior: attraction to a Mittag-Leffler process for $0<\alpha<1$, to a centered Cauchy process for $\alpha=1$ and to a stable process for $1<\alpha\leq 2$. Equivalently, in dynamical terms, almost every renewal path is, upon centering and up to a regularly varying coordinate change of order one, and after removing a set of times of Cesàro density zero, in the stable manifold of a self-similar path for the scaling flow. As a corollary we have pathwise functional and central limit theorems.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	CNPq, FAPERGS, FAPESP, CNRS, Cooperation Franco-Brazil.
7.	Date	(YYYY-MM-DD)	2011-05-10
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/888
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-888
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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