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In this paper, we are concerned with the limit theory of stochastic McKean–Vlasov equations. First, we prove the optimalLp{L^{p}}(p⩾2{p\geqslant 2}) strong convergence rate of the Wong–Zakai approximation for stochastic McKean–Vlasov equations. Then we show the support theorem for stochastic McKean–Vlasov equations.

Wong–Zakai approximations and support theorems for stochastic McKean–Vlasov equations