14 papers
Averaging Principle and Pullback Attractor Convergence for McKean--Vlasov Stochastic Reaction--Diffusion Equations
Honglei Chen, Mengyu Cheng, Zhenxin Liu
We establish three averaging principles for distribution-dependent stochastic reaction--diffusion equations with rapidly oscillating coefficients on the torus , $d\le3…
Continuity of measure-theoretic entropy for stochastic differential equations
Zhenxin Liu, Lixin Zhang
For stochastic differential equations, we establish a relationship between the measure-theoretic entropy of the stochastic flow and the rate of volume growth of stable submanifolds…
A criterion for the well-posedness of McKean-Vlasov stochastic differential equations
Zhenxin Liu, Ziting Liu
The paper provides criteria guaranteeing strong existence and pathwise uniqueness for McKean‑Vlasov stochastic differential equations under distribution‑dependent Lyapunov and hybr…
Convergence rates of Wasserstein gradient flows for nonlinear Fokker-Planck equations with mobility and related inequalities
Zhenxin Liu, Xuewei Wang
For nonlinear Fokker-Planck equations with mobility, the Wasserstein gradient flow structure is described by the generalized relative entropy as the energy functional and the modif…
Continuity and Discontinuity of McKean-Vlasov Phase Transitions via Bifurcation Theory
Junlang Hu, Zhenxin Liu
It is well known that the McKean-Vlasov stochastic differential equation with a symmetric double-well potential exhibits a continuous phase transition. In contrast, for an asymmetr…
Semimartingale Optimal Transport with Jumps: A General Framework and Equivalent Formulations
Boyi Hou, Zhenxin Liu
We study a semimartingale optimal transport (SOT) problem where the cost depends on the full differential characteristics, and the minimisation is over all semimartingale laws with…