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arXiv · 1502.05070

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

María J. Garrido-Atienza·Björn Schmalfuss·Kening Lu
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Abstract

We consider the stochastic evolution equation $ du=Audt+G(u)d\omega,\quad u(0)=u_0 $ in a separable Hilbert--space $V$. Here $G$ is supposed to be three times Fr\'echet--differentiable and $\omega$ is a trace class fractional Brownian--motion with Hurst parameter $H\in (1/3,1/2]$. We prove the existence of a global solution where exceptional sets are independent of the initial state $u_0\in V$. In addition, we show that the above equation generates a random dynamical system.

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María J. Garrido-Atienza, Björn Schmalfuss, Kening Lu. 2015-02-17. Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters $H\in (1/3,1/2]$. https://arxiv.org/abs/1502.05070

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