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On a SDE driven by a fractional Brownian motion and with monotone drift
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Brahim Boufoussi, Department of Mathematics, Cadi Ayyad University FSSM
Youssef Ouknine, Universite Cadi Ayyad
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Abstract
Let ${B_{t}^{H},tin lbrack 0,T]}$
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 $X_{t}=x+B_{t}^{H}+%
int_{0}^{t}left( b_{1}(s,X_{s})+b_{2}(s,X_{s})right) ds$, where $%
b_{1}(s,x)$ is a H"{o}lder 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.
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Full text: PDF
Pages: 122-134
Published on: October 7, 2003
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