Particle approximation for a conditional McKean--Vlasov stochastic differential equation
Probability
2024-03-27 v1
Abstract
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.
Cite
@article{arxiv.2403.17555,
title = {Particle approximation for a conditional McKean--Vlasov stochastic differential equation},
author = {Kai Du and Yunzhang Li and Yuyang Ye},
journal= {arXiv preprint arXiv:2403.17555},
year = {2024}
}