Quenched LDP for words in a letter sequence
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1349 | |
dc.contributor.author | Birkner, Matthias | |
dc.contributor.author | Greven, Andreas | |
dc.contributor.author | den Hollander, Frank | |
dc.date.accessioned | 2016-03-24T17:38:23Z | |
dc.date.available | 2019-06-28T08:03:18Z | |
dc.date.issued | 2008 | |
dc.description.abstract | When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. 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 the present paper we consider the quenched LDP, i.e., we condition on a typical letter sequence. We focus on the case where the renewal process has an algebraic tail. The rate function turns 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, with the former being obtained by concatenating the words and randomising the location of the origin. The proportionality constant equals the tail exponent of the renewal process. Earlier work by Birkner considered the case where the renewal process has an exponential tail, in which case the rate function turns out to be the first term on the set where the second term vanishes and to be infinite elsewhere ... | |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/3049 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2014 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.subject.ddc | 510 | |
dc.subject.other | Letters and words | eng |
dc.subject.other | renewal process | eng |
dc.subject.other | empirical process | eng |
dc.subject.other | annealed vs. quenched | eng |
dc.subject.other | large deviation principle | eng |
dc.subject.other | rate function | eng |
dc.subject.other | specific relative entropy | eng |
dc.subject.other | collision local time | eng |
dc.title | Quenched LDP for words in a letter sequence | |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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