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Functional Convergence to Stable Lévy Motions for Iterated Random Lipschitz Mappings

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Functional Convergence to Stable Lévy Motions for Iterated Random Lipschitz Mappings
2.	Creator	Author's name, affiliation, country	Sana Louhichi; Université Joseph Fourier; France
2.	Creator	Author's name, affiliation, country	Emmanuel Rio; Université de Versailles Saint-Quentin en Y.; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Partial sums processes. Skorohod topologies. Functional limit theorem. Association. Tightness. Ottaviani inequality. Stochastically monotone Markov chains. Iterated random Lipschitz mappings.
3.	Subject	Subject classification	Primary 60F17; 60J10; Secondary: 60F05;60G51;60G52
4.	Description	Abstract	It is known that, in the dependent case, partial sums processes which are elements of $D([0,1])$ (the space of right-continuous functions on $[0,1]$ with left limits) do not always converge weakly in the $J_1$-topology sense. The purpose of our paper is to study this convergence in $D([0,1])$ equipped with the $M_1$-topology, which is weaker than the $J_1$ one. We prove that if the jumps of the partial sum process are associated then a functional limit theorem holds in $D([0,1])$ equipped with the $M_1$-topology, as soon as the convergence of the finite-dimensional distributions holds. We apply our result to some stochastically monotone Markov chains arising from the family of iterated Lipschitz models.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-11-26
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/965
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-965
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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