187 citations · 727 across the 42 of their papers we have counts for
43 papers
McKean-Vlasov Stochastic Partial Differential Equations: Existence, Uniqueness and Propagation of Chaos
Wei Hong, Shihu Li, Wei Liu
In this paper, we provide a general framework for investigating McKean-Vlasov stochastic partial differential equations. We first show the existence of weak solutions by combining…
Large deviation principles for stochastic nonlinear Schrodinger equations driven by Levy noise
Jiahui Zhu, Wei Liu, Jianliang Zhai
In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic nonlinear Schrödinger equation, with either focusing or defocusing nonlinearity, driven…
McKean-Vlasov SDE and SPDE with Locally Monotone Coefficients
Wei Hong, Shanshan Hu, Wei Liu
In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness re…
Pathwise Blowup of space-time fractional SPDEs
Chang-Song Deng, Wei Liu, Erkan Nane
The finite time blowup in the almost sure sense of a class of space-time fractional stochastic partial differential equations is discussed. Both the cases of white noise and colore…
Weighted average values of automorphic -functions
Wei Liu
Let be the set of primitive Hecke eigenforms of weight 2 and prime level . For prime and , we prove asymptotic formulas for the sums $$ \mathcal…
Central Limit Type Theorem and Large Deviation Principle for Multi-Scale McKean-Vlasov SDEs
Wei Hong, Shihu Li, Wei Liu +1
In this paper, we aim to study the asymptotic behavior for multi-scale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviati…
Nonmonotone local minimax methods for finding multiple saddle points
Wei Liu, Ziqing Xie, Wenfan Yi
In this paper, by designing a normalized nonmonotone search strategy with the Barzilai--Borwein-type step-size, a novel local minimax method (LMM), which is a globally convergent i…
Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs
Wei Liu, Ziqing Xie, Wenfan Yi
The local minimax method (LMM) proposed in [Y. Li and J. Zhou, SIAM J. Sci. Comput., 23(3), 840--865 (2001)] and [Y. Li and J. Zhou, SIAM J. Sci. Comput., 24(3), 865--885 (2002)] i…
Strong Convergence Rates in Averaging Principle for Slow-Fast McKean-Vlasov SPDEs
Wei Hong, Shihu Li, Wei Liu
In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational…
Quantitative ergodic theorems for actions of groups of polynomial growth
Guixiang Hong, Wei Liu
We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational…
Large Deviation Principle for McKean-Vlasov Quasilinear Stochastic Evolution Equations
Wei Hong, Shihu Li, Wei Liu
This paper is devoted to investigating the Freidlin-Wentzell's large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We…
Distribution Dependent Stochastic Porous Media Equations
Jingyue Gao, Wei Hong, Wei Liu
Using the generalized variational framework, the strong/weak existence and uniqueness of solutions are derived for a class of distribution dependent stochastic porous media equatio…
Freidlin-Wentzell Type Large Deviation Principle for Multi-Scale Locally Monotone SPDEs
Wei Hong, Shihu Li, Wei Liu
This work is concerned with Freidlin-Wentzell type large deviation principle for a family of multi-scale quasilinear and semilinear stochastic partial differential equations. Emplo…
Truncated Milstein method for non-autonomous stochastic differential equations and its modification
Juan Liao, Wei Liu, Xiaoyan Wang
The truncated Milstein method, which was initially proposed in (Guo, Liu, Mao and Yue 2018), is extended to the non-autonomous stochastic differential equations with the super-line…
A minimax argument to a stronger version of the Jacobian conjecture
Wei Liu
The main result of this paper is to prove the strong real Jacobian conjecture under the symmetric assumption and reveals the link between it and the Jacobian conjecture. Precisely,…
Long-time behaviors of mean-field interacting particle systems related to McKean-Vlasov equations
Wei Liu, Liming Wu, Chaoen Zhang
In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric , uniform in the number of particle…
Finite Time Blowup of Solutions to SPDEs with Bernstein Functions of the Laplacian
Chan-Song Deng, Wei Liu, Erkan Nane
The blowup in finite time of solutions to SPDEs \begin{equation*} \partial_tu_t(x)=-ϕ(-Δ)u_t(x) +σ(u_t(x))\dotξ(t,x), \quad t>0,x\in\mathbb{R}^d, \end{equation*} { is} investigated…
The Stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise
Zdzisław Brzeźniak, Wei Liu, Jiahui Zhu
We establish a new version of the stochastic Strichartz estimate for the stochastic convolution driven by jump noise which we apply to the stochastic nonlinear Schrödinger equation…
The Kinetic Fokker-planck Equation With Mean Field Interaction
Arnaud Guillin, Wei Liu, Liming Wu +1
We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation. We prove a uniform (in…
Well-posedness of Backward Stochastic Partial Differential Equations with Lyapunov Condition
Wei Liu, Rongchan Zhu
In this paper we show the existence and uniqueness of strong solutions for a large class of backward SPDE where the coefficients satisfy a specific type Lyapunov condition instead…
Small Time Asymptotics for SPDEs with Locally Monotone Coefficients
Shihu Li, Wei Liu, Yingchao Xie
This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial differential equations (SPDEs) with locally monotone coefficients in genera…
Uniform Poincar{é} and logarithmic Sobolev inequalities for mean field particles systems
Arnaud Guillin, Wei Liu, Liming Wu +1
In this paper we establish some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, w…
Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations
Wei Liu, Michael Röckner, José Luís da Silva
In this paper strong dissipativity of generalized time-fractional derivatives on Gelfand triples of properly in time weighted -path spaces is proved. In particular, the classi…
Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods
Zhenyu Bao, Jingwen Tang, Yan Shen +1
In this paper, a general theorem on the equivalence of pth moment stability between stochastic differential delay equations (SDDEs) and their numerical methods is proved under the…