Continuous Ocone Martingales as Weak Limits of Rescaled Martingales
نویسندگان
چکیده
منابع مشابه
Continuous Martingales and Local Martingales
Throughout these notes, (Ω,F ,P ) will be a probability space and F := {Ft }t∈J a filtration indexed by J , where J is an interval, usually J = [0,∞). The filtration F is said to be complete if each Ft contains all sets of measure 0, and is right-continuous if Ft =∩s>t Fs . A standard filtration is a filtration that is both complete and right-continuous. A stochastic process {X t }t≥0 defined o...
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© Springer-Verlag, Berlin Heidelberg New York, 1976, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...
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We present a framework for the construction of Weitzenböck and ClarkOcone formulae for differential forms on the probability space of a normal martingale. This approach covers existing constructions based on Brownian motion, and extends them to other normal martingales such as compensated Poisson processes. It also applies to the path space of Brownian motion on a Lie group and to other geometr...
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Given a sequence (M)n=1 of non-negative martingales starting at M n 0 = 1 we find a sequence of convex combinations (M̃)n=1 and a limiting process X such that (M̃n τ ) ∞ n=1 converges in probability to Xτ , for all finite stopping times τ . The limiting process X then is an optional strong supermartingale. A counter-example reveals that the convergence in probability cannot be replaced by almost ...
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© Springer-Verlag, Berlin Heidelberg New York, 1985, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2002
ISSN: 1083-589X
DOI: 10.1214/ecp.v7-1062