Nonlinear McKean-Vlasov diffusions under the weak Hörmander condition with quantile-dependent coefficients. (English) Zbl 07815299
Summary: 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 Hörmander condition. The approach relies on the a priori 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.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
Keywords:
McKean-Vlasov equation; Langevin equation; weak Hörmander condition; Feynman-Kac formula; two-sided Gaussian estimates; quantile-dependent PDEReferences:
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