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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 *** also propose a framework for verifying hyper-exponential recurrence,and apply it to study the large deviation problems for strong dissipative *** 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 of stochastic differential equations with non-Lipschitzian coefficients

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Frontiers of Mathematics in China 2013年第6期8卷 1307-1321页

作者： Guangqiang LAN School of Science Beijing University of Chemical Technology Beijing 100029 China

We study the large deviation principle of stochastic differential equations with non-Lipschitzian and non-homogeneous coefficients. We consider at first the large deviation principle when the coefficients σ and b are bounded, then we generalize the conclusion to unbounded case by using bounded approximation program. Our results are generalization of S. Fang-T. Zhang＇s results.

关键词： Stochastic differential equation non-Lipschitzian large deviation principle

large deviation principle for diffusion processes under a sublinear expectation

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Science China Mathematics 2012年第11期55卷 2205-2216页

作者： CHEN ZengJing 1,2 & XIONG Jie 3,4,1 School of Mathematics,Shandong University,Jinan 250100,China 2 Department of Financial Engineering,Ajou University,Suwon 443749,Korea 3 Department of Mathematics,University of Macao,PO Box 3001,Macao,China 4 Department of Mathematics,University of Tennessee,Knoxville,TN 37996-1300,USA 1. School of Mathematics Shandong University Jinan 250100 China 2. Department of Financial Engineering Ajou University Suwon 443749 Korea 3. Department of Mathematics University of Macau PO Box 3001 Macau China 4. Department of Mathematics University of Tennessee Knoxville TN 37996-1300 USA

We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential *** an application,we establish a large deviation principle of the Freidlin and Wentzell type under the corresponding nonlinear probability for diffusion processes with a small diffusion coefficient.

关键词： large deviation principle backward stochastic differential equation g-expectation ambiguity

large deviation principle for the Two-dimensional Stochastic Navier-Stokes Equations with Anisotropic Viscosity

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Acta Mathematicae Applicatae Sinica 2023年第3期39卷 511-549页

作者： Bing-guang CHEN Xiang-chan ZHU Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Department of Mathematics University of BielefeldD-33615 BielefeldGermany

In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short *** proof for large deviation principle is based on the weak convergence *** small time asymptotics we use the exponential equivalence to prove the result.

关键词： large deviation principle stochastic Navier-Stokes equations anisotropic viscosity small time asymptotics weak convergence approach

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

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 *** main difficulties come from the highly non-linear coefficient and the jump ***,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

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≤*** 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,*** recovers some well-known ***,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 *** 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

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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 300071 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