Synchronization by noise for stochastic differential equations driven by fractional Brownian motion
Abstract
We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index H∈(0,1). Provided that the SDE has a negative top Lyapunov exponent, we show that a weak form of synchronization occurs. To this aim we use tools from stochastic dynamical systems, random dynamical systems and characterize the support of an invariant measure of a random dynamical system in a non-Markovian setting.
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