@article{Fischer2013345,
    Abstract = {There exists a simple, didactically useful one-to-one relationship between stopping times and adapted c{\`a}dl{\`a}g (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.},
    Author = {Fischer, Tom},
    File = {On simple representations of stopping times and stopping time sigma-algebras - Fischer (0) (0) - a - a - g.pdf},
    ISSN = {0167-7152},
    Journal = {Statistics \& Probability Letters},
    Keywords = {D{\'e}but Theorem},
    Number = {1},
    Pages = {345 - 349},
    Title = {On simple representations of stopping times and stopping time sigma-algebras},
    URL = {http://www.sciencedirect.com/science/article/pii/S0167715212003707},
    Volume = {83},
    Year = {2013},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0167715212003707},
    bdsk-url-2 = {http://dx.doi.org/10.1016/j.spl.2012.09.024},
    date-added = {2014-06-12 04:24:38 +0000},
    date-modified = {2014-06-12 04:24:38 +0000},
    doi = {10.1016/j.spl.2012.09.024}
}

@article{Fischer2013345, Abstract = {There exists a simple, didactically useful one-to-one relationship between stopping times and adapted c{`a}dl{`a}g (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.}, Author = {Fischer, Tom}, File = {On simple representations of stopping times and stopping time sigma-algebras - Fischer (0) (0) - a - a - g.pdf}, ISSN = {0167-7152}, Journal = {Statistics \& Probability Letters}, Keywords = {D{\'e}but Theorem}, Number = {1}, Pages = {345 - 349}, Title = {On simple representations of stopping times and stopping time sigma-algebras}, URL = {http://www.sciencedirect.com/science/article/pii/S0167715212003707}, Volume = {83}, Year = {2013}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0167715212003707}, bdsk-url-2 = {http://dx.doi.org/10.1016/j.spl.2012.09.024}, date-added = {2014-06-12 04:24:38 +0000}, date-modified = {2014-06-12 04:24:38 +0000}, doi = {10.1016/j.spl.2012.09.024} }