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RASE1: Recent Advances in Stochastic Equations: Regularity, Numerical analysis, and Dynamical Behavior Location: L602 Session Chair: Giacomo Lucertini | |
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Bifurcations for SPDEs driven by fBM Universität Konstanz, Germany We study noise-induced transitions in a non-autonomous double-well potential driven by fractional Brownian motion with Hurst parameter $H \in (1/2,1)$. Extending the sample-path approach from the Brownian to the non-Markovian setting, we investigate the behaviour of solutions near stable equilibrium branches in the small-noise regime. To recover a Markovian framework, we employ the Markovian lift and consider the associated stochastic dynamical system on an enlarged state space. This allows us to formulate suitable tube events and derive probabilistic estimates via the transition semigroup of the lifted process. Our main results provide pathwise concentration estimates around stable deterministic branches and identify Hurst-dependent transition scales. In particular, the classical Brownian scaling laws are replaced by fractional counterparts reflecting the long-range dependence of the driving noise. These estimates yield quantitative bounds on the probability of remaining in neighbourhoods of stable equilibria and describe the onset of noise-induced transitions in the strong-noise regime. The results constitute a first step towards a sample-path theory of stochastic resonance and dynamic bifurcations for systems driven by fractional Brownian motion. | |
