Multiplicative ergodic theorem for a non-irreducible random dynamical system - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Journal of Differential Equations Year : 2020

Multiplicative ergodic theorem for a non-irreducible random dynamical system

Abstract

We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplicative ergodic theorem with an exponential rate of convergence. The assumptions are satisfied for a large class of parabolic PDEs, including the 2D Navier–Stokes and complex Ginzburg–Landau equations perturbed by a non-degenerate bounded random kick force. As a consequence of this ergodic theorem, we derive some new results on the statistical properties of the trajectories of the underlying random dynamical system. In particular, we obtain large deviations principle for the occupation measures and the analyticity of the pressure function in a setting where the system is not irreducible. The proof relies on a refined version of the uniform Feller property combined with some contraction and bootstrap arguments.
Fichier principal
Vignette du fichier
1801.09440.pdf (407.25 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03993050 , version 1 (28-01-2018)
hal-03993050 , version 2 (20-01-2020)
hal-03993050 , version 3 (16-03-2023)

Identifiers

Cite

Davit Martirosyan, Vahagn Nersesyan. Multiplicative ergodic theorem for a non-irreducible random dynamical system. Journal of Differential Equations, 2020, 268 (7), pp.3564-3598. ⟨10.1016/j.jde.2019.10.002⟩. ⟨hal-03993050v3⟩
529 View
259 Download

Altmetric

Share

More