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Zbl 1035.60056
Eisenbaum, Nathalie; Hu, Yueyun
A family of integral representations for the Brownian variables. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 39, No. 6, 1083-1096 (2003). ISSN 0246-0203

The natural filtration of a real Brownian motion and its excursion filtration are sharing the property of integral representation, and thus, each Brownian variable admits two distinct integral representations. It is shown that there are other integral representations of the Brownian variables. The authors make use of a stochastic flow studied by Bass and Burdzy. The arguments are inspired by Rogers and Walsh's results on stochastic integration with respect to the Brownian local times.
[Pavel Gapeev (Moskva)]

MSC 2000:: *60H05 Stochastic integrals
60G44 Martingales with continuous parameter
60J65 Brownian motion

Keywords: Brownian motion; integral representation; flow; area integral

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