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The idea behind the question arises from my intuition about the concepts of 'adapted to filtration' and 'previsbility'.

If a process is adapted, it essentially means that the evolution of the universe upto time t reveals the history of our process upto time t also.

On the other hand, if a process is previsible, it means that the evolution of the universe upto time t reveals information about the process beyond time t.

If we are thinking in these terms, it becomes natural to ask if we can construct processes where the evolution of the universe upto time t reveals information about such processes only upto a time prior to t, say t-1.

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