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Weak solutions to stochastic differential equations driven by fractional Brownian motion

J. Šnupárková — 2009

Czechoslovak Mathematical Journal

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 ∈ ( 0 , 1 ) ∖ { 1 2 } 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

Bohdan Maslowski;  J. Šnupárková — 2018

Applications of Mathematics

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 1 / 2 . 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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