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Keywords:
fractional Brownian motion; Girsanov theorem; weak solutions
fractional Brownian motion; Girsanov theorem; weak solutions
Summary:
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.
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