Finite-time Lyapunov exponents for SPDEs with fractional noise

21 Sep 2023 · Alexandra Blessing, Dirk Blömker ·

We estimate the finite-time Lyapunov exponents for a stochastic partial differential equation driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$ 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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Finite-time Lyapunov exponents for SPDEs with fractional noise

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