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Concerning the geometry of stochastic differential equations and stochastic flows

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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

Topics: QA
Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD
OAI identifier: oai:wrap.warwick.ac.uk:15076
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