Flow of Homeomorphisms and Stochastic Transport Equations
- 30 August 2007
- journal article
- research article
- Published by Taylor & Francis Ltd in Stochastic Analysis and Applications
- Vol. 25 (5), 1079-1108
- https://doi.org/10.1080/07362990701540568
Abstract
We consider Stratonovich stochastic differential equations with drift coefficient A 0 satisfying only the condition of continuity where r is a positive C 1 function defined on a neighborhood ]0, c 0] of 0 such that (Osgood condition), and s → r(s) is decreasing while s → sr(s 2) is increasing. We prove that the equation defines a flow of homeomorphisms if the diffusion coefficients A 1,…, A N are in . If , we prove limit theorems for Wong–Zakai approximation as well as for regularizing the drift A 0. As an application, we solve a class of stochastic transport equations.Keywords
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