Tail behaviour of stationary densities for one-dimensional random diffeomorphisms

2024/10/24 by Jeroen S. W. Lamb, Lamb, Jeroen S. W., Guillermo Olicón-Méndez +3 · 1 citation
Mathematics · Physics and Astronomy · #37A50 #37C30 #37H20 #60G10 #60J05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2410.18554

openalex publication_date 2024/10/24 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of stationary densities of one-dimensional random diffeomorphisms, at the boundaries of their support, which correspond to deterministic fixed points of extremal diffeomorphisms. In particular, we show how this stationary density at a boundary depends on the underlying noise distribution, as well as the linearisation of the extremal diffeomorphism at the boundary point (in case the corresponding fixed point is hyperbolic), or the leading nonlinear term of the extremal diffeomorphism (in case the corresponding fixed point is not hyperbolic).

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• Anticipating bifurcations of random dynamical systems through tails of stationary densities

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