Markovian reduction and exponential mixing in total variation for random dynamical systems
Probability
2025-07-15 v1 Classical Analysis and ODEs
Dynamical Systems
Abstract
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure in the total variation metric. The proof is based on the Markovian reduction of the system in question and a result on mixing for Markov processes. Then we present an extension of this result to the case of systems driven by stationary noises.
Cite
@article{arxiv.2507.09707,
title = {Markovian reduction and exponential mixing in total variation for random dynamical systems},
author = {Sergei Kuksin and Armen Shirikyan},
journal= {arXiv preprint arXiv:2507.09707},
year = {2025}
}