Continuous dependence for McKean-Vlasov SDEs under distribution-dependent Lyapunov conditions

Abstract: In this paper, we consider the continuous dependence on initial values and parameters of solutions as well as invariant measures for McKean-Vlasov SDEs under distribution-dependent Lyapunov conditions. In contrast to the classical SDEs, the solutions for McKean-Vlasov SDEs do not converge in probability although the initial values converge in probability, which is due to the mismatch of the distances between measures. Finally, we give some examples to illustrate our theoretical results.