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A large deviation principle FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE

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Acta Mathematica Scientia 2023年第2期43卷 505-530页

作者：王冉张贝贝 School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).

关键词： large deviation principle weak convergence method stochastic generalized Ginzburg-Landau equation Poisson random measure

large deviation principle for a class of SPDE with locally monotone coefficients

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Science China Mathematics 2020年第6期63卷 1181-1202页

作者： Wei Liu Chunyan Tao Jiahui Zhu School of Mathematics and Statistics Jiangsu Normal UniversityXuzhou 221116China School of Science Zhejiang University of TechnologyHangzhou 310023China

This work aims to prove the large deviation principle for a class of stochastic partial differential equations with locally monotone coefficients under the extended variational framework, which generalizes many previous works. Using stochastic control and the weak convergence approach, we prove the Laplace principle,which is equivalent to the large deviation principle in our framework. Instead of assuming compactness of the embedding in the corresponding Gelfand triple or finite dimensional approximation of the diffusion coefficient in some existing works, we only assume some temporal regularity in the diffusion coefficient.

关键词： stochastic partial differential equation large deviation principle Laplace principle weak convergence approach locally monotone

large deviation principle of occupation measures for non-linear monotone SPDEs

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Science China Mathematics 2021年第4期64卷 799-822页

作者： Ran Wang Jie Xiong Lihu Xu School of Mathematics and Statistics Wuhan UniversityWuhan 430072China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Department of Mathematics Faculty of Science and TechnologyUniversity of MacaoMacaoChina

Using the hyper-exponential recurrence criterion,we establish the occupation measures’large deviation principle for a class of non-linear monotone stochastic partial differential equations(SPDEs)driven by Wiener noise,including the stochastic p-Laplace equation,the stochastic porous medium equation and the stochastic fast-diffusion equation.We also propose a framework for verifying hyper-exponential recurrence,and apply it to study the large deviation problems for strong dissipative SPDEs.These SPDEs can be stochastic systems driven by heavy-tailedα-stable process.

关键词： stochastic partial differential equation large deviation principle occupation measure hyperexponential recurrence

large deviation principle for the Fourth-order Stochastic Heat Equations with Fractional Noises

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Acta Mathematica Sinica,English Series 2010年第1期26卷 89-106页

作者： Yi Ming JIANG Ke Hua SHI Yong Jin WANG School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 P. R. China

In this paper, we shall study a fourth-order stochastic heat equation driven by a fractional noise, which is fractional in time and white in space. We will discuss the existence and uniqueness of the solution to the equation. Furthermore, the regularity of the solution will be obtained. On the other hand, the large deviation principle for the equation with a small perturbation will be established through developing a classical method.

关键词： fourth-order stochastic heat equation fractional noise existence and uniqueness regularity large deviation principle

large deviation principle for a Form of Compound Nonhomogeneous Poisson Process

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Journal of Donghua University(English Edition) 2011年第2期28卷 217-221页

作者：杨文权胡亦钧 School of Mathematics and Computer Science Jianghan University School of Mathematics and Statistics Wuhan University

By the Cramér method, the large deviation principle for a form of compound Poisson process S(t)=∑N(t)i=1h(t-Si)Xi is obtained,where N(t), t>0, is a nonhomogeneous Poisson process with intensity λ(t)>0, Xi, i≥1, are i.i.d. nonnegative random variables independent of N(t), and h(t), t>0, is a nonnegative monotone real function. Consequently, weak convergence for S(t) is also obtained.

关键词： large deviation principle compound Poisson process weak convergence

Unified Limits and large deviation principles forβ-Laguerre Ensembles in Global Regime

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Acta Mathematica Sinica,English Series 2023年第7期39卷 1271-1288页

作者： Yu Tao MA School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems of Ministry of Education Beijing Normal UniversityBeijing 100875China

Let(λ_(1),...,λ_(n)) be β-Laguerre ensembles with parametersβ,p,n and μ_(n):=1/n∑^(n)_(i=1)δ_(Xi) with for 1≤i≤n.In this paper,asβvaries and satisfies lim_(n→∞)log n/βn=0,we offer a modified Marchenko-Pastur,law or semicircle law as the weak limits for the sequence μ_(n) when lim_(n→∞)n/p=γ∈(0,1]or lim_(n→∞)n/p=0,respectively.This recovers some well-known results.Moreover,we give a full large deviation principle of μ_(n) with speed βn^(2) and good rate function I_(γ) under the same condition to characterize the speed of the convergence.The minimizer of I_(γ) is a modified Marchenko-Pastur law forγ∈(0,1]and the semicircle law forγ=0.

关键词： β-Laguerre ensemble large deviation principle empirical measure semicircular law Marchenko–Pastur law

large deviation for Stochastic Cahn-Hilliard Partial Differential Equations

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Acta Mathematica Sinica,English Series 2009年第7期25卷 1157-1174页

作者： Ke Hua SHI Dan TANG Yong Jin WANGSchool of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China School of Mathematical Sciences Nankai University Tianjin P. R. China

In this paper, we prove a large deviation principle for a class of stochastic Cahn-Hilliard partial differential equations driven by space-time white noises.

关键词： stochastic Cahn-Hilliard partial differential equations large deviation principle Freidlin Wentzell inequality

SIMPLE PROOF OF A large deviation RESULT

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 326-331页

作者：张志祥 School of Mathematical Sciences Peking University Beijing China

In this note we prove a large deviation result for a perturbed discontinuous inhomogeneous system which complements[1].

关键词： large deviation principle stochastic differential equation contraction principle Donsker's invariance principle

Limit Theorems and large deviations forβ-Jacobi Ensembles at Scaling Temperatures

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Acta Mathematica Sinica,English Series 2023年第10期39卷 2054-2074页

作者： Yu Tao MA School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems of Ministry of Education Beijing Normal UniversityBeijing 100875P.R.China

Letλ=(λ_(1),...,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβwhileβvarying with n.Setγ=lim_(n→∞)n/p_(1)andσ=lim_(n→∞)p_(1)/p_(2).In this paper,supposing lim_(n→∞)log_(n)/β_(n)=0,we prove that the empirical measures of different scaledλconverge weakly to a Wachter distribution,a Marchenko–Pastur law and a semicircle law corresponding toσγ>0,σ=0 orγ=0,respectively.We also offer a full large deviation principle with speedβn^(2)and a good rate function to precise the speed of these convergences.As an application,the strong law of large numbers for the extremal eigenvalues ofβ-Jacobi ensembles is obtained.

关键词： β-Jacobi ensemble large deviation principle semi-circle law Marchenko-Pastur law Wachter law