2016/05/03 by Aurélien Deya, Deya, Aurélien, Fabien Panloup +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1605.00880
openalex publication_date 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the problem of the rate of convergence to equilibrium for\nergodic stochastic differential equations driven by fractional Brownian motion\nwith Hurst parameter H\∈ (1/3,1) and multiplicative noise component\n\σ. When \σ is constant and for every H\∈ (0,1), it was proved\nin [19] that, under some mean-reverting assumptions, such a process converges\nto its equilibrium at a rate of order t-\α where \α \∈ (0,1)\n(depending on H). In [11], this result has been extended to the\nmultiplicative case when H textgreater1/2. In this paper, we obtain these\ntypes of results in the rough setting H\∈ (1/3,1/2). Once again, we retrieve\nthe rate orders of the additive setting. Our methods also extend the\nmultiplicative results of [11] by deleting the gradient assumption on the noise\ncoefficient \σ. The main theorems include some existence and uniqueness\nresults for the invariant distribution.\n