Rate of convergence to equilibrium of fractional driven stochastic differential equations with some multiplicative noise

Abstract : We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H>1/2$ and multiplicative noise component $\sigma$. When $\sigma$ is constant and for every $H\in(0,1)$, it was proved in \cite{hairer} that, under some mean-reverting assumptions, such a process converges to its equilibrium at a rate of order $t^{-\alpha}$ where $\alpha\in(0,1)$ (depending on $H$). The aim of this paper is to extend such types of results to some multiplicative noise setting. More precisely, we show that we can recover such convergence rates when $H>1/2$ and the inverse of the diffusion coefficient $\sigma$ is a Jacobian matrix. The main novelty of this work is a type of extension of Foster-Lyapunov like techniques to this non-Markovian setting, which allows us to put in place an asymptotic coupling scheme such as in \cite{hairer} without resorting to deterministic contracting properties.
Type de document :
Pré-publication, Document de travail
2014
Liste complète des métadonnées

Littérature citée [20 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00989414
Contributeur : Fabien Panloup <>
Soumis le : jeudi 14 janvier 2016 - 16:29:15
Dernière modification le : samedi 16 janvier 2016 - 01:10:40
Document(s) archivé(s) le : samedi 16 avril 2016 - 11:01:12

Fichiers

ergodicity_multiplicative_fBm_...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00989414, version 2
  • ARXIV : 1405.2573

Collections

Citation

Joaquin Fontbona, Fabien Panloup. Rate of convergence to equilibrium of fractional driven stochastic differential equations with some multiplicative noise. 2014. 〈hal-00989414v2〉

Partager

Métriques

Consultations de
la notice

208

Téléchargements du document

52