AN EXPLICIT MILSTEIN-TYPE SCHEME FOR INTERACTING PARTICLESYSTEMS AND MCKEAN-VLASOV SDES WITH COMMON NOISE ANDNON-DIFFERENTIABLE DRIFT COEFFICIENTS

• 成果类型: Article
• 署名作者: Biswas, Sani; Kumar, Chaman; Neelima; Dos Reis, Goncalo; Reisinger, Christoph
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Roorkee; University of Delhi; University of Edinburgh; University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2024
• 发表日期: 2024
• 页码: 2326-2363
• 关键词: equations; propagation; simulation; systems; limit

摘要

We propose an explicit drift-randomised Milstein scheme for bothMcKean-Vlasov stochastic differential equations and associated high-dimen-sional interacting particle systems with common noise. By using a driftrandomisation step in space and measure, we establish the scheme's strongconvergence rate of 1 under reduced regularity assumptions on the drift co-efficient: no classical (Euclidean) derivatives in space or measure derivatives(e.g., Lions/Frechet) are required. The main result is established by enrich-ing the concepts of bistability and consistency of numerical schemes usedpreviously for standard SDE. We introduce certain Spijker-type norms (andassociated Banach spaces) to deal with the interaction of particles present inthe stochastic systems being analysed. A discussion of the scheme's com-plexity is provided.