Stochastic bilinear equations with fractional Gaussian noise in Hilbert space
Weak solutions to stochastic differential equations driven by fractional Brownian motion
Existence of a weak solution to the -dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter 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.
Stochastic affine evolution equations with multiplicative fractional noise
A stochastic affine evolution equation with bilinear noise term is studied, where the driving process is a real-valued fractional Brownian motion with Hurst parameter greater than . Stochastic integration is understood in the Skorokhod sense. The existence and uniqueness of weak solution is proved and some results on the large time dynamics are obtained.
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