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Some Remarks on Davie’s Uniqueness Theorem

Part of: Equations and systems with randomness Miscellaneous applications of functional analysis Stochastic analysis

Published online by Cambridge University Press:  16 March 2016

A. V. Shaposhnikov
A. V. Shaposhnikov*
Affiliation:
Department of Mechanics and Mathematics, Moscow State University, 119991 Moscow, Russia ([email protected])
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Abstract

We present a new approach to Davie’s theorem on the uniqueness of solutions to the equation

for almost all Brownian paths. A generalization of this result and a discussion of some closely related problems are given.

Keywords

Brownian motionstochastic differential equationpathwise uniqueness

MSC classification

Secondary: 60H10: Stochastic ordinary differential equations 34F05: Equations and systems with randomness 46N20: Applications to differential and integral equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 4 , November 2016 , pp. 1019 - 1035
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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