Electronic Communications in Probability

On a SDE driven by a fractional Brownian motion and with monotone drift

Brahim Boufoussi and Youssef Ouknine

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Abstract

Let ${B_{t}^{H},t\in \lbrack 0,T]}$ be a fractional Brownian motion with Hurst parameter $H \gt \frac{1}{2}$. We prove the existence of a weak solution for a stochastic differential equation of the form $X_{t}=x+B_{t}^{H}+ \int_{0}^{t}\left( b_{1}(s,X_{s})+b_{2}(s,X_{s})\right) ds$, where $ b_{1}(s,x)$ is a Holder continuous function of order strictly larger than $1-\frac{1}{2H}$ in $x$ and than $H-\frac{1}{2}$ in time and $b_{2}$ is a real bounded nondecreasing and left (or right) continuous function.

Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 14, 122-134.

Dates
Accepted: 7 October 2003
First available in Project Euclid: 18 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463608898

Digital Object Identifier
doi:10.1214/ECP.v8-1084

Mathematical Reviews number (MathSciNet)
MR2042751

Zentralblatt MATH identifier
1060.60060

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G18: Self-similar processes

Keywords
Fractional Brownian motion Stochastic integrals Girsanov transform

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Boufoussi, Brahim; Ouknine, Youssef. On a SDE driven by a fractional Brownian motion and with monotone drift. Electron. Commun. Probab. 8 (2003), paper no. 14, 122--134. doi:10.1214/ECP.v8-1084. https://projecteuclid.org/euclid.ecp/1463608898


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