Smooth invariant densities for random switching on the torus
Dynamical Systems
2018-03-22 v2 Probability
Abstract
We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector fields are transversal to each other at all points of the torus and that each of them allows for a smooth invariant density and no periodic orbits, we prove that the switched system also has a smooth invariant density, for every switching rate. Our approach is based on an integration by parts formula inspired by techniques from Malliavin calculus.
Cite
@article{arxiv.1708.01390,
title = {Smooth invariant densities for random switching on the torus},
author = {Yuri Bakhtin and Tobias Hurth and Sean D. Lawley and Jonathan C. Mattingly},
journal= {arXiv preprint arXiv:1708.01390},
year = {2018}
}
Comments
19 pages