Asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise

Abstract

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of non-autonomous fractional stochastic lattice systems with multiplicative noise. The considered systems are driven by the fractional discrete Laplacian, which features the infinite-range interactions. We first prove the existence of pullback random attractor in <inline-formula><tex-math id="M1">\begin{document}$ \ell^2 $\end{document}</tex-math></inline-formula> for stochastic lattice systems. The upper semicontinuity of random attractors is also established when the intensity of noise approaches zero.</p>

Limiting behavior of invariant measures for stochastic delay nonlocallattice dynamical systems

“…Chen and Wang [9] proved the existence and upper semicontinuity of the attractors to fractional stochastic lattice systems with linear multiplicative noise. In this paper, we will examine the limiting behavior of invariant measures for the stochastic delay fractional lattice systems when ε → ε 0 ∈ [0, 1] and ρ → 0, respectively.…”