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arXiv · 1903.01702

Setvalued dynamical systems for stochastic evolution equations driven by fractional noise

M. J. Garrido-Atienza·B. Schmalfuss·J. Valero
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Abstract

We consider Hilbert-valued evolution equations driven by H\"{o}lder paths with H\"{o}lder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2,1). The assumptions of the drift term will not be enough to ensure the uniqueness of solutions. Nevertheless, adopting a multivalued setting, we will prove that the set of all solutions corresponding to the same initial condition generates a (multivalued) nonautonomous dynamical system $\Phi$. Finally, to prove that $\Phi$ is measurable (and hence a (multivalued) random dynamical system), we need to construct a new metric dynamical system that models the noise with the property that the set space is separable

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M. J. Garrido-Atienza, B. Schmalfuss, J. Valero. 2019-03-05. Setvalued dynamical systems for stochastic evolution equations driven by fractional noise. https://arxiv.org/abs/1903.01702

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