2022/08/22 by Sani Biswas, Biswas, Sani, Chaman Kumar +7 · 3 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #60H35 #65C05 #65C30 #65C35 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA) #Probability (math.PR) #Statistical Methods and Bayesian Inference #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2208.10052
openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an explicit drift-randomised Milstein scheme for both McKean--Vlasov stochastic differential equations and associated high-dimensional interacting particle systems with common noise. By using a drift-randomisation step in space and measure, we establish the scheme's strong convergence rate of 1 under reduced regularity assumptions on the drift coefficient: no classical (Euclidean) derivatives in space or measure derivatives (e.g., Lions/Fréchet) are required. The main result is established by enriching the concepts of bistability and consistency of numerical schemes used previously for standard SDE. We introduce certain Spijker-type norms (and associated Banach spaces) to deal with the interaction of particles present in the stochastic systems being analysed. A discussion of the scheme's complexity is provided.