Setvalued Dynamical Systems for Stochastic Evolution Equations Driven by Fractional Noise

We consider Hilbert-valued evolution equations driven by Hölder paths with Hölder 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...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2022-03, Vol.34 (1), p.79-105
Main Authors: Garrido-Atienza, M. J., Schmalfuss, B., Valero, J.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Dynamical systems
Evolution
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:We consider Hilbert-valued evolution equations driven by Hölder paths with Hölder 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 Φ . Finally, to prove that Φ 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.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-019-09811-9