Filtrations of the Erased-Word Processes

We define a class of erased-word processes and prove that the poly-adic filtration generated by such a process is standard. This is shown by firstly constructing a generating process of innovations in the case of a finite alphabet equipped with the uniform probability measure, and then by deriving t...

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Bibliographic Details
Published inSéminaire de Probabilités XLVIII Vol. 2168; pp. 445 - 458
Main Author Laurent, Stéphane
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2016
Springer International Publishing
SeriesLecture Notes in Mathematics
Subjects
Finite Alphabet
Level Criterion
Probability & statistics
Probability Vector
Product Type
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Summary:We define a class of erased-word processes and prove that the poly-adic filtration generated by such a process is standard. This is shown by firstly constructing a generating process of innovations in the case of a finite alphabet equipped with the uniform probability measure, and then by deriving the general case with the help of the tools of Vershik’s theory of filtrations in discrete negative time.
ISBN:9783319444642
3319444646
ISSN:0075-8434
1617-9692
DOI:10.1007/978-3-319-44465-9_16