From the 1 of 17 linked papers with an AI index.
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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…
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…
Random Attractors for McKean-Vlasov SDEs
Mengyu Cheng, Xianjin Cheng, Zhenxin Liu
In this paper, we mainly focus on the existence of random attractors for McKean-Vlasov stochastic differential equations on a separable Hilbert space . A significant challenge a…
Quenched invariance principle with a rate for random dynamical systems
Zhenxin Liu, Benoit Saussol, Sandro Vaienti +1
In this paper, we consider the quenched invariance principle for random Young towers driven by an ergodic system. In particular, we obtain the Wassertein convergence rate in the qu…
Invariant measures for stochastic Burgers equation on unbounded domains
Zhenxin Liu, Zhiyuan Shi
In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mil…