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Flow of diffeomorphisms induced by a geometric multiplicative functional
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  • Published: September 1998

Flow of diffeomorphisms induced by a geometric multiplicative functional

  • Terry Lyons1 &
  • Zhongmin Qian1 

Probability Theory and Related Fields volume 112, pages 91–119 (1998)Cite this article

  • 145 Accesses

  • 18 Citations

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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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Authors and Affiliations

  1. Department of Mathematics, Huxley Building, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, London SW7 2BZ, UK e-mail: t.lyons@ic.ac.uk; z.qian@ic.ac.uk, , , , , , GB

    Terry Lyons & Zhongmin Qian

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  1. Terry Lyons
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  2. Zhongmin Qian
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Received: 6 May 1996 / Revised version: 20 March 1998

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Cite this article

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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  • Issue Date: September 1998

  • DOI: https://doi.org/10.1007/s004400050184

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  • Mathematics Subject Classification(1991): Primary 60D05
  • 58D25
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