Mean field analysis of interacting network model with jumps  

带跳跃的交互网络模型的平均场分析

作　　者：Zeqian Li 李泽乾(中国科学技术大学数学科学学院,安徽合肥230026)

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《中国科学技术大学学报》2024年第8期14-23,13,I0002,共12页JUSTC

摘　　要：This study considers an-particle jump-diffusion system with mean field interaction,where the coefficients are locally Lipschitz continuous.We address the convergence as n→∞of the empirical measure of the jump-diffusions to the solution of a deterministic McKean-Vlasov equation.The strong well-posedness of the associated McKean-Vlasov equation and a corresponding propagation of chaos result are proven.In particular,we also provide precise estimates of the convergence speed with respect to a Wasserstein-like metric.本文考虑具有平均场交互作用的n粒子跳跃扩散模型,其中系数是局部Lipschitz连续的。研究了当n→∞时跳跃扩散的经验测度到McKean-Vlasov方程的解之间的收敛。证明了相关的McKean-Vlasov方程强解的适定性以及混沌传播结果。特别地,基于一种类似于Wasserstein度量的距离,还提供了收敛速度的精确估计。

关 键 词：mean field theory McKean-Vlasov equations FPK equations propagation of chaos particle system 

分 类 号：O211.63[理学—概率论与数理统计]