Markovian reduction and exponential mixing in total variation for random dynamical systems

Sergei Kuksin; Armen Shirikyan

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arXiv · 2507.09707

Markovian reduction and exponential mixing in total variation for random dynamical systems

Sergei Kuksin·Armen Shirikyan

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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.

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BibTeX RIS

Sergei Kuksin, Armen Shirikyan. 2025-07-13. Markovian reduction and exponential mixing in total variation for random dynamical systems. https://arxiv.org/abs/2507.09707

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