Measure Attractors of Stochastic Fractional Lattice Systems

This paper seeks to establish the measure attractors in stochastic fractional lattice systems. First, the presence of these attractor measures is proven by the uniform estimates of the solution. Subsequently, the study also looks at the upper semicontinuous dependence of the measure attractors on the noise intensity as the latter goes to zero. The given asymptotic compactness for the family of probability measures occurring with the solution probability distributions is exhibited by a uniform prior estimation of the far-field solution values.