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Stochastic Integration

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Continuous Martingales and Brownian Motion

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 293))

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Abstract

In this chapter, we introduce some basic techniques and notions which will be used throughout the sequel. Once and for all, we consider below, a filtered probability space (Ω, F, F t , P) and we suppose that each F t contains all the sets of P-measure zero in F. As a result, any limit (almost-sure, in the mean, etc.) of adapted processes is an adapted process; a process which is indistinguishable from an adapted process is adapted.

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Notes and Comments

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Authors and Affiliations

  1. Départment de Mathématiques, Université Paris VII, 2, place Jussieu, 75251, Paris Cedex 05, France

    Daniel Revuz

  2. Laboratoire de Probabilités, Université Pierre et Marie Curie, 4, place Jussieu, Boîte courrier 188, 75252, Paris Cedex 05, France

    Marc Yor

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  1. Daniel Revuz
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  2. Marc Yor
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© 1999 Springer-Verlag Berlin Heidelberg

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Revuz, D., Yor, M. (1999). Stochastic Integration. In: Continuous Martingales and Brownian Motion. Grundlehren der mathematischen Wissenschaften, vol 293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06400-9_5

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  • DOI: https://doi.org/10.1007/978-3-662-06400-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08400-3

  • Online ISBN: 978-3-662-06400-9

  • eBook Packages: Springer Book Archive

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