Rate of convergence to equilibrium for discrete-time stochastic dynamics with memory
Résumé
The main objective of the paper is to study the long-time behavior of general discrete dynamics driven by ergodic stationary Gaussian noise. To this end, we first explain how is it possible to define invariant distributions in this generally non-Markovian setting and to get existence results under appropriate conditions. Then, we get a uniqueness result and a rate of convergence to the invariant distribution in total variation thanks to a coupling procedure (with a step specific to non-Markovian framework).
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