Geodesic
Weak solutions to stochastic differential equations driven by fractional Brownian motion
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 879-907 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Existence of a weak solution to the $n$-dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter $H\in (0,1)\setminus \{\frac 12\}$ is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.
Existence of a weak solution to the $n$-dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter $H\in (0,1)\setminus \{\frac 12\}$ is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.
Classification : 60G22, 60H10
Keywords: fractional Brownian motion; Girsanov theorem; weak solutions 
@article{CMJ_2009_59_4_a2,
     author = {\v{S}nup\'arkov\'a, J.},
     title = {Weak solutions to stochastic differential equations driven by fractional {Brownian} motion},
     journal = {Czechoslovak Mathematical Journal},
     pages = {879--907},
     year = {2009},
     volume = {59},
     number = {4},
     mrnumber = {2563565},
     zbl = {1224.60149},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a2/}
}
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Šnupárková, J. Weak solutions to stochastic differential equations driven by fractional Brownian motion. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 879-907. http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a2/