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Développement des distributions suivant les chaos de Wiener et applications a l’analyse stochastique. (Developement of distributions along the Wiener chaos and applications to stochastic analysis). (French) Zbl 0621.60048

Sémin. probabilités XXI, Lect. Notes Math. 1247, 27-32 (1987).
[For the entire collection see Zbl 0606.00022.]
In this note we show that Meyer’s formal expansion of generalized Wiener functionals in the Watanabe sense [see P. A. Meyer and the author, A propos des distributions sur l’espace de Wiener, ibid. 8-26 (1987)] can be applied to stochastic analysis. As an example, we give a simple proof of a recent result of A. S. Ustunel [Representation of the distributions on Wiener space and stochastic calculus of variation. Preprint] about the representation of generalized Wiener functionals which is an extension of Clark’s theorem [J. M. C. Clark, Ann. Math. Stat. 41, 1282-1295 (1970; Zbl 0213.194); Corrections ibid. 42, 1778 (1971)].

MSC:

60G20 Generalized stochastic processes
60J65 Brownian motion
60H99 Stochastic analysis
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