Asymptotic behavior of stochastic Schrödinger lattice systems driven by nonlinear noise. Issue 2 (3rd March 2020)

• Record Type: Journal Article
• Authors: Wang, Bixiang; Wang, Renhai
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 2(2020)
• Page Start: 213
• Page End: 237
• Publication Date: 2020-03-03
• Subjects: Weak random attractor -- invariant measure -- noise -- lattice system -- stochastic Schrödinger equation; Primary 37L55 -- Secondary 34F05 -- 37L30 -- 60H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1679646
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: We study the random dynamics of the N -dimensional stochastic Schrödinger lattice systems with locally Lipschitz diffusion terms driven by locally Lipschitz nonlinear noise. We first prove the existence and uniqueness of solutions and define a mean random dynamical system associated with the solution operators. We then establish the existence and uniqueness of weak pullback random attractors in a Bochner space. We finally prove the existence of invariant measures of the stochastic equation in the space of complex-valued square-summable sequences. The tightness of a family of probability distributions of solutions is derived by the uniform estimates on the tails of the solutions at far field.