标题： 粒子近似用于条件麦凯恩-弗拉索夫随机微分方程 显示英文标题

标题： Particle approximation for a conditional McKean--Vlasov stochastic differential equation

摘要： 在本文中，我们构建了一类相互作用粒子系统来近似一类随机微分方程，其系数依赖于给定部分观测的进程的条件概率分布。 在证明了粒子系统的适定性和正则性之后，我们建立了当粒子数量增加时，粒子系统经验测度在Wasserstein空间中的定量收敛结果。 此外，我们讨论了粒子系统的Euler--Maruyama方案并验证了其强收敛性。 进行了一个数值实验来说明我们的结果。 显示英文摘要

摘要： In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations. After proving the well-posedness and regularity of the particle systems, we establish a quantitative convergence result for the empirical measures of the particle systems in the Wasserstein space, as the number of particles increases. Moreover, we discuss an Euler--Maruyama scheme of the particle system and validate its strong convergence. A numerical experiment is conducted to illustrate our results.