RANDOM ATTRACTORS FOR SECOND ORDER STOCHASTIC LATTICE DYNAMICAL SYSTEMS WITH MULTIPLICATIVE NOISE IN WEIGHTED SPACES

摘要

In this paper, we study the asymptotic behavior of solutions of a second order stochastic lattice differential equation with multiplicative white noise in weighted spaces. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then establish the existence of tempered random bounded absorbing sets and global random attractors.