For a stochastic nonautonomous Korteweg–de Vries lattice system with superlinear noise, we study evolutionary probability measures on Banach spaces \(l^p\) for \(2<p<2.5\) . We construct an evolution system of measures with finite measure norms. We then introduce the concept of a measure kernel section at current time and show that all measure kernel sections are nonempty, tight, closed and convex. Moreover, we establish the upper semicontinuity of the measure kernel sections with respect to the intensity of superlinear noise. Ito’s formulas of higher-order polynomials play key roles to prove the asymptotic tightness of distribution laws.
