Euler simulation of interacting particle systems and McKean–Vlasov SDEs with fully super-linear growth drifts in space and interaction

Abstract This work addresses the convergence of a split-step Euler type scheme (SSM) for numerical simulation interacting particle Stochastic Differential Equation (SDE) systems and McKean–Vlasov stochastic differential equations (MV-SDEs) with full super-linear growth in spatial interaction component drift, nonconstant Lipschitz diffusion coefficient. Super-linearity is understood sense that functions are assumed to behave polynomially, but also satisfy so-called one-sided condition. The (or measure) stems from convolution operations functions, allowing particular application granular media equation multi-well confining potentials. From methodological point view, we avoid altogether functional inequality arguments (as allow nonbounded maps). attains, stepsize, near-optimal classical (path-space) root mean-square error rate $1/2-\varepsilon $ $\varepsilon>0$ an optimal $1/2$ nonpath-space (pointwise) metric. All findings illustrated by examples. In particular, testing raises doubts if taming suitable methodology this problem (with terms coefficients).