Setvalued dynamical systems for stochastic evolution equations driven by fractional noise

2019/03/05 by María J. Garrido–Atienza, Garrido-Atienza, M. J., Björn Schmalfuß +3
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1903.01702

openalex publication_date 2019/03/05 · openalex created_date 2019/03/11 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Random dynamical systems
• RANDOM ATTRACTORS FOR STOCHASTIC EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION

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