The Filtration of the split-words process

Abstract

M. Smorodinsky and S. 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.