Electronic Communications in Probability

Stochastic flows of diffeomorphisms for one-dimensional SDE with discontinuous drift

Stefano Attanasio

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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.

Article information

Electron. Commun. Probab., Volume 15 (2010), paper no. 20, 213-226.

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

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]

Stochastic flows Local time

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Attanasio, Stefano. Stochastic flows of diffeomorphisms for one-dimensional SDE with discontinuous drift. Electron. Commun. Probab. 15 (2010), paper no. 20, 213--226. doi:10.1214/ECP.v15-1545. https://projecteuclid.org/euclid.ecp/1465243963

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