Nonlinear McKean-Vlasov diffusions under the weak Hormander condition with quantile-dependent coefficients
Probability
2021-03-15 v2
Abstract
In this paper, the strong existence and uniqueness for a degenerate finite system of quantile-dependent McKean-Vlasov stochastic differential equations are obtained under a weak H\"{o}rmander condition. The approach relies on the apriori bounds for the density of the solution to time inhomogeneous diffusions. The time inhomogeneous Feynman-Fac formula is used to construct a contraction map for this degenerate system.
Cite
@article{arxiv.2101.04080,
title = {Nonlinear McKean-Vlasov diffusions under the weak Hormander condition with quantile-dependent coefficients},
author = {Yaozhong Hu and Michael A. Kouritzin and Jiayu Zheng},
journal= {arXiv preprint arXiv:2101.04080},
year = {2021}
}