Abstract
We construct the Doob-Meyer decomposition of a submartingale as a pointwise superior limit of decompositions of discrete submartingales suitably built upon discretizations of the original process. This gives, in particular, a direct proof of predictability of the increasing process in the Doob-Meyer decomposition.
Adam Jakubowski: Supported by Komitet Badań Naukowychunder Grant No PB 0253/P03/2000/19 and completed while the author was visiting Université de Rouen.The author would like to thank people of Mathematics in Rouen for their hospitality.
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© 2005 Springer-Verlag Berlin/Heidelberg
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Jakubowski, A. (2005). An Almost Sure Approximation for the Predictable Process in the Doob-Meyer Decomposition Theorem. In: Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVIII. Lecture Notes in Mathematics, vol 1857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31449-3_11
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DOI: https://doi.org/10.1007/978-3-540-31449-3_11
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