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On simple representations of stopping times and stopping time sigma-algebras

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  • Fischer, Tom
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    Abstract

    There exists a simple, didactically useful one-to-one relationship between stopping times and adapted càdlàg (RCLL) processes that are non-increasing and take the values 0 and 1 only. As a consequence, stopping times are always hitting times. Furthermore, we show how minimal elements of a stopping time sigma-algebra can be expressed in terms of the minimal elements of the sigma-algebras of the underlying filtration. This facilitates an intuitive interpretation of stopping time sigma-algebras. A tree example finally illustrates how these for students notoriously difficult concepts, stopping times and stopping time sigma-algebras, may be easier to grasp by means of our results.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212003707
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 1 ()
    Pages: 345-349

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:345-349

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    Related research

    Keywords: Début Theorem; Hitting time; Stopped sigma-algebra; Stopping time; Stopping time sigma-algebra;

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