Entropy-cost type Propagation of Chaos for Mean Field Particle System with Bounded Measurable Interaction

Abstract: In this paper, the quantitative entropy-cost type propagation of chaos for mean field interacting particle system is obtained, where the interaction is only assumed to be bounded measurable and the initial distribution of a single particle converges to that of the corresponding McKean-Vlasov SDEs in $L^1$-transportation cost $\W_1^\Psi$ induced by some cost function $\Psi$. The mean field interacting particle system with common noise is also investigated and the quantitative entropy-cost type conditional propagation of chaos is established. The results weaken the initial assumption of the existing entropy-entropy type propagation of chaos in some sense.