Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model. (15th February 2016)

• Record Type: Journal Article
• Authors: Andreis, Luisa; Barbato, David; Collet, Francesca; Formentin, Marco; Provenzano, Luigi
• Is Part Of: Nonlinearity. Volume 29:Number 3(2016:Mar.)
• Page Start: 1156
• Page End: 1169
• Publication Date: 2016-02-15
• Subjects: inviscid dyadic model -- infinite dimensional system of SDEs -- pathwise uniqueness -- strong solution -- strong statistically stationary solution; 37L55 -- 37N10 -- 35Q31; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/3/1156
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution.