PULLBACK MEASURE ATTRACTORS AND LIMITING BEHAVIORS OF MCKEAN-VLASOV STOCHASTIC DELAY LATTICE SYSTEMS

The paper proves existence and uniqueness of D-pullback measure attractors for a McKean–Vlasov stochastic delay lattice system on ℓ2, via (i) well-posedness, (ii) weighted L2/L4 moment estimates to build a tempered absorbing family in P4(Cr), (iii) D-pullback asymptotic compactness using time-modulus and tail-end estimates plus Arzelà–Ascoli, and (iv) a general pullback-attractor theorem on Polish spaces. It further derives singleton attractors and exponential mixing under a one-sided coercivity. The candidate solution follows the same blueprint and matches the technical structure, including the same function spaces, absorbing-set construction, tightness mechanism (time-modulus + spatial tails), and the contraction/mixing corollary. Minor differences are mainly expository: the paper carefully restricts continuity of the cocycle to bounded subsets via Vitali’s theorem, whereas the model states continuity more broadly but implicitly uses the same moment control. No substantive logical conflict was found.