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Concerning the geometry of stochastic differential equations and stochastic flows
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UNSPECIFIED (1997) Concerning the geometry of stochastic differential equations and stochastic flows. In: Taniguchi International Workshop on New Trends in Stochastic Analysis, CHARINGWORTH, ENGLAND, SEP 21-27, 1994. Published in: NEW TRENDS IN STOCHASTIC ANALYSIS pp. 107-131. ISBN 981-02-2867-8.
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Abstract
Le Jan and Watanabe showed that a non-degenerate stochastic flow {xi(t) : t greater than or equal to 0} on a manifold M determines a connection on M. This connection is characterized here and shown to be the Levi-Civita connection for gradient systems. This both explains why such systems have useful properties and allows us to extend these properties to more general systems. Topics described here include: moment estimates for T xi(t), a Weitzenbock formula for the generator of the semigroup on p-forms induced by the flow, a Bismut type formula for d log p(t) in terms of an arbitrary metric connection, and a generalized Bochner vanishing theorem.
Item Type: | Conference Item (UNSPECIFIED) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | NEW TRENDS IN STOCHASTIC ANALYSIS | ||||
Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD | ||||
ISBN: | 981-02-2867-8 | ||||
Editor: | Elworthy, KD and Kusuoka, S and Shigekawa, I | ||||
Official Date: | 1997 | ||||
Dates: |
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Number of Pages: | 25 | ||||
Page Range: | pp. 107-131 | ||||
Publication Status: | Published | ||||
Title of Event: | Taniguchi International Workshop on New Trends in Stochastic Analysis | ||||
Location of Event: | CHARINGWORTH, ENGLAND | ||||
Date(s) of Event: | SEP 21-27, 1994 |
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