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On a SDE driven by a fractional Brownian motion and with monotone drift. (English) Zbl 1060.60060

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.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G18 Self-similar stochastic processes
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