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The filtration of the split-words process
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  • Published: 13 September 2011

The filtration of the split-words process

  • Gaël Ceillier1 

Probability Theory and Related Fields volume 153, pages 269–292 (2012)Cite this article

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Abstract

Smorodinsky and Laurent have initiated the study of the filtrations of split-word processes, in the framework of discrete negative time. For these filtrations, we show that Laurent’s sufficient condition for non standardness is also necessary, thus yielding a practical standardness criterion. In turn, this criterion enables us to exhibit a non standard filtration which becomes standard when time is accelerated by omitting infinitely many instants of time.

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Authors and Affiliations

  1. Institut Fourier, UMR CNRS 5582, UFR de Mathématiques, Université Grenoble I, BP 74, 100 Rue des Maths, 38402, St Martin d’Hères cedex, France

    Gaël Ceillier

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  1. Gaël Ceillier
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Correspondence to Gaël Ceillier.

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Ceillier, G. The filtration of the split-words process. Probab. Theory Relat. Fields 153, 269–292 (2012). https://doi.org/10.1007/s00440-011-0346-7

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  • Received: 05 July 2010

  • Revised: 06 January 2011

  • Published: 13 September 2011

  • Issue Date: June 2012

  • DOI: https://doi.org/10.1007/s00440-011-0346-7

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Mathematics Subject Classification (2000)

  • 60G15
  • 60A99
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