Boufoussi, Brahim; Ouknine, Youssef On a SDE driven by a fractional Brownian motion and with monotone drift. (English) Zbl 1060.60060 Electron. Commun. Probab. 8, 122-134 (2003). Summary: Let \(\{B_{t}^{H}\), \(t\in [ 0,T]\}\) be a fractional Brownian motion with Hurst parameter \(H>\frac{1}{2}\). We prove the existence of a weak solution for a stochastic differential equation of the form \(X_{t}=x+B_{t}^{H}+ \int_{0}^{t}( b_{1}(s,X_{s})+ b_{2}(s,X_{s}))\, ds\), where \( b_{1}(s,x)\) is a Hölder 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. Cited in 1 ReviewCited in 14 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60G18 Self-similar stochastic processes Keywords:fractional Brownian motion; stochastic integrals; Girsanov transform PDFBibTeX XMLCite \textit{B. Boufoussi} and \textit{Y. Ouknine}, Electron. Commun. Probab. 8, 122--134 (2003; Zbl 1060.60060) Full Text: DOI EuDML