Tail behaviour of stationary densities for one-dimensional random diffeomorphisms
Probability
2024-10-25 v1 Dynamical Systems
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).
Cite
@article{arxiv.2410.18554,
title = {Tail behaviour of stationary densities for one-dimensional random diffeomorphisms},
author = {Jeroen S. W. Lamb and Guillermo Olicón-Méndez and Martin Rasmussen},
journal= {arXiv preprint arXiv:2410.18554},
year = {2024}
}