Abstract.
In this paper it is shown that the unique multiplicative functional solution to a differential equation driven by a geometric multiplicative functional consitutes a flow of local diffeomorphisms. In the case where the driving geometric multiplicative functional is generated by a Brownian motion, the result in particular presents an answer to an open problem proposed in Ikeda and Watanabe [4].
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Received: 6 May 1996 / Revised version: 20 March 1998
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Lyons, T., Qian, Z. Flow of diffeomorphisms induced by a geometric multiplicative functional. Probab Theory Relat Fields 112, 91–119 (1998). https://doi.org/10.1007/s004400050184
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DOI: https://doi.org/10.1007/s004400050184