Flow of diffeomorphisms induced by a geometric multiplicative functional

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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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APA

Lyons, T., & Qian, Z. (1998). Flow of diffeomorphisms induced by a geometric multiplicative functional. Probability Theory and Related Fields, 112(1), 91–119. https://doi.org/10.1007/s004400050184

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