Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters H∈ (1/3,1/2]

2015/02/17 by María J. Garrido–Atienza, Garrido-Atienza, María 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.1502.05070

openalex publication_date 2015/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the stochastic evolution equation du=Audt+G(u)dω, u(0)=u₀ in a separable Hilbert--space V. Here G is supposed to be three times Fréchet--differentiable and ω is a trace class fractional Brownian--motion with Hurst parameter H∈ (1/3,1/2]. We prove the existence of a global solution where exceptional sets are independent of the initial state u₀∈ V. In addition, we show that the above equation generates a random dynamical system.

Citations

• Lévy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces

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