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Limit theorems for Parrondo's paradox

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Limit theorems for Parrondo's paradox
2.	Creator	Author's name, affiliation, country	S N Ethier; University of Utah
2.	Creator	Author's name, affiliation, country	Jiyeon Lee; Yeungnam University
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Parrondo's paradox, Markov chain, strong law of large numbers, central limit theorem, strong mixing property, fundamental matrix, spectral representation.
3.	Subject	Subject classification	Primary 60J10; secondary 60F05.
4.	Description	Abstract	That there exist two losing games that can be combined, either by random mixture or by nonrandom alternation, to form a winning game is known as Parrondo's paradox. We establish a strong law of large numbers and a central limit theorem for the Parrondo player's sequence of profits, both in a one-parameter family of capital-dependent games and in a two-parameter family of history-dependent games, with the potentially winning game being either a random mixture or a nonrandom pattern of the two losing games. We derive formulas for the mean and variance parameters of the central limit theorem in nearly all such scenarios; formulas for the mean permit an analysis of when the Parrondo effect is present.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Yeungnam University
7.	Date	(YYYY-MM-DD)	2009-09-02
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/684
10.	Identifier	Digital Object Identifier	10.1214/EJP.v14-684
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 14
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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