2022/08/26 by Xingyuan Chen, Gonçalo dos Reis, Chen, Xingyuan +1 · 6 citations
Economics, Econometrics and Finance · Mathematics · #65C05 #65C30 #65C35 #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2208.12772
openalex publication_date 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider in this work the convergence of a split-step Euler type scheme (SSM) for the numerical simulation of interacting particle Stochastic Differential Equation (SDE) systems and McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with full super-linear growth in the spatial and the interaction component in the drift, and non-constant Lipschitz diffusion coefficient. The super-linear growth in the interaction (or measure) component stems from convolution operations with super-linear growth functions allowing in particular application to the granular media equation with multi-well confining potentials. From a methodological point of view, we avoid altogether functional inequality arguments (as we allow for non-constant non-bounded diffusion maps). The scheme attains, in stepsize, a near-optimal classical (path-space) root mean-square error rate of 1/2-ε for ε>0 and an optimal rate 1/2 in the non-path-space mean-square error metric. Numerical examples illustrate all findings. In particular, the testing raises doubts if taming is a suitable methodology for this type of problem (with convolution terms and non-constant diffusion coefficients).