## Electronic Communications in Probability

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

Stefano Attanasio

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.ecp/1465243963

Digital Object Identifier
doi:10.1214/ECP.v15-1545

Mathematical Reviews number (MathSciNet)
MR2653726

Zentralblatt MATH identifier
1226.60086

Keywords
Stochastic flows Local time

Rights

#### Citation

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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