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2001 | OriginalPaper | Buchkapitel

Nonnegative Supermartingales and Martingales, and the Girsanov Theorem

verfasst von : Robert S. Liptser, Albert N. Shiryaev

Erschienen in: Statistics of Random Processes

Verlag: Springer Berlin Heidelberg

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Let (Ω, F, P) be a complete probability space, and let (F t ), 0 ≤t≤T, be a nondecreasing family of sub-σ-algebras of F, augmented by sets from F of probability zero. Let W = (W t , F t ) be a Wiener process and let γ = (γ t , F t ) be a random process with 6.1$$P\left( {\int {_0^T} \gamma _s^2ds \infty } \right) = 1.$$

Metadaten
Titel
Nonnegative Supermartingales and Martingales, and the Girsanov Theorem
verfasst von
Robert S. Liptser
Albert N. Shiryaev
Copyright-Jahr
2001
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-13043-8_7