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