Finite-time Lyapunov exponents for SPDEs with fractional noise

2023/09/21 by Blessing, Alexandra, Blömker, Dirk · 2 citations
#37H15 #37H20 #60H10 #60H15 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.12189

Abstract

We estimate the finite-time Lyapunov exponents for a stochastic partial differential equation driven by a fractional Brownian motion (fbm) with Hurst index H∈(0,1) close to a bifurcation of pitchfork type. We characterize regions depending on the distance from bifurcation, the Hurst parameter of the fbm and the noise strength where finite-time Lyapunov exponents are positive and thus indicate a change of stability. The results on finite-time Lyapunov exponents are novel also for SDEs perturbed by fractional noise.

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