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Large deviation principles for words drawn from correlated letter sequences

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Large deviation principles for words drawn from correlated letter sequences
2.	Creator	Author's name, affiliation, country	Frank den Hollander; Leiden Universiteit; Netherlands
2.	Creator	Author's name, affiliation, country	Julien Poisat; Leiden Universiteit; Netherlands
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Letters and words, renewal times, empirical process, annealed vs. quenched large deviation principle, rate function, specific relative entropy, mixing
3.	Subject	Subject classification	60F10; 60G10
4.	Description	Abstract	When an i.i.d. sequence of letters is cut into words according to i.i.d. renewal times, an i.i.d.\ sequence of words is obtained. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In Birkner, Greven and den Hollander, the quenched LDP (= conditional on a typical letter sequence) was derived for the case where the renewal times have an algebraic tail. The rate function turned out to be a sum of two terms, one being the annealed rate function, the other being proportional to the specific relative entropy of the observed law of letters w.r.t. the reference law of letters, obtained by concatenating the words and randomising the location of the origin. The proportionality constant equals the tail exponent of the renewal process. The purpose of the present paper is to extend both LDP's to letter sequences that are not i.i.d. It is shown that both LDP's carry over when the letter sequence satisfies a mixing condition called summable variation. The rate functions are again given by specific relative entropies w.r.t. the reference law of words, respectively, letters. But since neither of these reference laws is i.i.d., several approximation arguments are needed to obtain the extension.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ERC Advanced Grant 267356 VARIS
7.	Date	(YYYY-MM-DD)	2014-03-01
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/2681
10.	Identifier	Digital Object Identifier	10.1214/ECP.v19-2681
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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