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

Tom Fischer

Statistics & Probability Letters, 2013, vol. 83, issue 1, 345-349

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.

Keywords: Début Theorem; Hitting time; Stopped sigma-algebra; Stopping time; Stopping time sigma-algebra (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:83:y:2013:i:1:p:345-349

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DOI: 10.1016/j.spl.2012.09.024

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