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2010 Stochastic flows of diffeomorphisms for one-dimensional SDE with discontinuous drift
Stefano Attanasio
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Electron. Commun. Probab. 15: 213-226 (2010). DOI: 10.1214/ECP.v15-1545

Abstract

The existence of a stochastic flow of class $C^{1,\alpha}$, for $\alpha < 1/2$, for a 1-dimensional SDE will be proved under mild conditions on the regularity of the drift. The diffusion coefficient is assumed constant for simplicity, while the drift is an autonomous BV function with distributional derivative bounded from above or from below. To reach this result the continuity of the local time with respect to the initial datum will also be proved.

Citation

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Stefano Attanasio. "Stochastic flows of diffeomorphisms for one-dimensional SDE with discontinuous drift." Electron. Commun. Probab. 15 213 - 226, 2010. https://doi.org/10.1214/ECP.v15-1545

Information

Accepted: 9 June 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1226.60086
MathSciNet: MR2653726
Digital Object Identifier: 10.1214/ECP.v15-1545

Subjects:
Primary: 60H10

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