In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion coefficients. We establish a propagation of chaos result, based on which the McKean-Vlasov equation is approximated by an interacting particle system. A truncated Euler scheme is then proposed for the interacting particle system allowing for a Khasminskii-type condition on the coefficients. To reduce the computational cost, the random batch approximation proposed in [Jin et al., J. Comput. Phys., 400(1), 2020] is extended to the interacting particle system where the interaction could take place in the diffusion term. An almost half order of convergence is proved in $L^p$ sense. Numerical tests are performed to verify the theoretical results.

翻译：本文提出了一种数值方法来求解McKean-Vlasov方程（一类分布依赖型随机微分方程），其中漂移系数和扩散系数均满足非全局Lipschitz条件。我们建立了混沌传播结果，并基于此将McKean-Vlasov方程近似为一个相互作用粒子系统。针对该相互作用粒子系统，我们提出了一个截断欧拉格式，该格式允许系数满足Khasminskii型条件。为降低计算成本，我们将[Jin等人，J. Comput. Phys., 400(1), 2020]中提出的随机批处理近似方法推广至相互作用可能出现在扩散项中的粒子系统。在L^p意义下证明了近半阶收敛性。通过数值实验验证了理论结果。