16 citations · 58 across the 27 of their papers we have counts for
16 papers · 1 filter
Sequential propagation of chaos
Kai Du, Yifan Jiang, Xiaochen Li
A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting p…
Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise
Kai Du, Ruoyang Liu, Yuxing Wang
Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative no…
Empirical approximation to invariant measures for McKean--Vlasov processes: mean-field interaction vs self-interaction
Kai Du, Yifan Jiang, Jinfeng Li
This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some pro…
Krylov-Safonov estimates for a degenerate diffusion process
Fu Zhang, Kai Du
This paper proves a Krylov-Safonov estimate for a multidimensional diffusion process whose diffusion coefficients are degenerate on the boundary. As applications the existence and…
Schauder-type estimates for higher-order parabolic SPDEs
Yuxing Wang, Kai Du
In this paper we consider the Cauchy problem for -order stochastic partial differential equations of parabolic type in a class of stochastic Hoelder spaces. The Hoelder estimat…
Optimal gradient estimates of heat kernels of stable-like operators
Kai Du, Xicheng Zhang
In this note we show the optimal gradient estimate for heat kernels of stable-like operators by providing a counterexample.