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A Gaussian process approximation for two-color randomly reinforced urns

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1.	Title	Title of document	A Gaussian process approximation for two-color randomly reinforced urns
2.	Creator	Author's name, affiliation, country	Lixin Zhang; Zhejiang University; China
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Reinforced urn model; Gaussian process; strong approximation; functional central limit theorem; P\'olya urn
3.	Subject	Subject classification	60F15;62G10;60F05;60F10
4.	Description	Abstract	The Polya urn has been extensively studied and is widely applied in many disciplines. An important application  is to use urn models to develop randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed. In this paper, we prove a Gaussian process approximation for the sequence of random composotions of a two-color randomly reinforced urn for both the cases with the equal and unequal reinforcement means. The Gaussian process is a tail stochastic integral with respect to  a Brownian motion. By using the Gaussian approximation, the law of the iterated logarithm and the functional  central limit theorem in both the stable convergence sense and the almost-sure conditional convergence sense are established. Also as a consequence, we are able to prove that the limit distribution of the normalized urn composition has no points masses both  when the reinforcements means are equal and unequal under the assumption of only finite $(2+\epsilon)$-th moments.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Zhejiang University
7.	Date	(YYYY-MM-DD)	2014-09-18
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/3432
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3432
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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