Rate of convergence to equilibrium for discrete-time stochastic dynamics with memory

Maylis Varvenne (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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).

Mots clés: Discrete stochastic dynamics; Stationary Gaussian noise; Rate of convergence to equilibrium; Total variation distance; Lyapunov function; Toeplitz operator

Domaines: Probabilités [math.PR]

Maylis Varvenne. Rate of convergence to equilibrium for discrete-time stochastic dynamics with memory. 2017. ⟨hal-01588505v2⟩