Semicontinuous evolution systems of enlarged measures for superlinear stochastic porous media lattice equations

For a stochastic nonautonomous porous media lattice equation driven by superlinear noise, we investigate its evolution systems of (enlarged) probability measures on the Banach [Formula: see text]-space for [Formula: see text] rather than the usual Hilbert [Formula: see text]-space, where the former space contains the latter. We prove the existence of an evolution system of enlarged measures. We then establish the upper semicontinuity of the section set of all evolution systems of enlarged measures at current time with respect to the noise intensity. Ito’s formulas for higher power functions play key roles in proving the pullback asymptotic property of enlarged solutions and the pullback asymptotic tightness of enlarged distribution laws.