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....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).展开更多
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...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.展开更多
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 e...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.展开更多
We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential equation.As an application,we establish a large deviation p...We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential equation.As 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.展开更多
In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x...In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.展开更多
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 previo...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.展开更多
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-Pas...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.展开更多
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 time.The proof for large deviation ...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 time.The proof for large deviation principle is based on the weak convergence approach.For small time asymptotics we use the exponential equivalence to prove the result.展开更多
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 nois...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.展开更多
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...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.展开更多
Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.
We prove the large deviation principle for the law of the one-dimensional semi-linear stochastic partial differential equations driven by a nonlinear multiplicative noise.Firstly,combining the energy estimate and appr...We prove the large deviation principle for the law of the one-dimensional semi-linear stochastic partial differential equations driven by a nonlinear multiplicative noise.Firstly,combining the energy estimate and approximation procedure,we obtain the existence of the global solution.Secondly,the large deviation principle is obtained via the weak convergence method.展开更多
Recently, the online social networks have emerged as one of the important platforms for social users. Among millions of users, famous person from entertainment circle arouse our interest. They promote social relations...Recently, the online social networks have emerged as one of the important platforms for social users. Among millions of users, famous person from entertainment circle arouse our interest. They promote social relationship and establish their reputation via these platforms. To analyze the social influence of entertainment stars we propose and implement a public cloud based framework to crawl celebrities' social messages from Sina Weibo, store the gathered messages and conduct various analysis to assess the socia influence. It consist of three key components: task generation, resource management and task scheduling, and influence analysis. The task generation is responsible of acquiring celebrities' socia accounts and issue crawling tasks. We propose a cross-media method to extract social accounts from webpages. The resource management and task scheduling will dynamic adjust the rented resource to minimize the total computing cost while keeping Qo S. We propose a dynamic instance provisioning strategy based on the large deviation principle. The influence analysis will undertake various types of analysis, such as fan count, posting frequency, textual analysis, and so on. More than 10,000 celebrities' microblogs have been gathered so far, and some related gainers, such as celebrities and ad agencies can gain the illumination brought by our analysis.展开更多
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.
This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems. We prove that the level-2 empirical process satisfies the large deviation ...This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems. We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology, while it does not satisfy the large deviation principles in the τ-topology.展开更多
From the perspective of Markovian piecewise deterministic processes(PDPs),we investigate the derivation of a kinetic uncertainty relation(KUR),which was originally proposed in Markovian open quantum systems.First,stat...From the perspective of Markovian piecewise deterministic processes(PDPs),we investigate the derivation of a kinetic uncertainty relation(KUR),which was originally proposed in Markovian open quantum systems.First,stationary distributions of classical PDPs are explicitly constructed.Then,a tilting method is used to derive a rate functional of large deviations.Finally,based on an improved approximation scheme,we recover the KUR.These classical results are directly extended to the open quantum systems.We use a driven two-level quantum system to exemplify the quantum results.展开更多
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...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.展开更多
We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution...We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.展开更多
In this paper,we establish a large deviation principle for two-dimensional primitive equations driven by multiplicative Lévy noises.The proof is based on the weak convergence approach.
基金partially supported by the National Natural Science Foundation of China(11871382,12071361)partially supported by the National Natural Science Foundation of China(11971361,11731012)。
文摘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).
基金National Natural Science Foundation of China(No. 10971157)Educational Commission of Hubei Province, China(No.2004X124)
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No. 10871103)
文摘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.
基金supported by National Natural Science Foundation of China (Grant No.10921101)WCU program of the Korea Science and Engineering Foundation (Grant No. R31-20007)National Science Foundation of US (Grant No. DMS-0906907)
文摘We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential equation.As 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.
基金Partially supported by NSFC(No.11701304)the K.C.Wong Education Foundation。
文摘In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.
基金National Natural Science Foundation of China (Grant Nos. 11501147, 11501509, 11822106 and 11831014)the Natural Science Foundation of Jiangsu Province (Grant No. BK20160004)the Qing Lan Project and the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘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.
基金Supported by NSFC(Grant Nos.12171038,11871008)the National Key R&D Program of China(Grant No.2020YFA0712900)985 Projects。
文摘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.
基金Research supported in part by NSFC(No.11771037)Key Lab of Random Complex Structures and Data Science,Chinese Academy of ScienceFinancial the DFG through the CRC 1283“Taming uncertainty and profiting from randomness and low regularity in analysis,stochastics and their applications”。
文摘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 time.The proof for large deviation principle is based on the weak convergence approach.For small time asymptotics we use the exponential equivalence to prove the result.
基金supported by National Natural Science Foundation of China(Grant Nos.11431014 and 11671076)supported by University of Macao Multi-Year Research Grant(Grant No.MYRG2016-00025-FST)Science and Technology Development Fund,Macao SAR(Grant Nos.025/2016/A1,030/2016/A1 and 038/2017/A1)the Faculty of Science and Technology,University of Macao,for financial support and hospitality。
文摘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.
文摘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.
基金Supported by the National Basic Research Program of China (973 Program,Grant No.2007CB814901)the National Natural Science Foundation of China (Grant No.10826098)+1 种基金the Natural Science Foundation of Anhui Province (Grant No.090416225)Anhui Natural Science Foundation of Universities (Grant No.KJ2010A037)
文摘Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.
基金supported in part by the NSFC Grant No.12171084the fundamental Research Funds for the Central Universities No.2242022R10013.
文摘We prove the large deviation principle for the law of the one-dimensional semi-linear stochastic partial differential equations driven by a nonlinear multiplicative noise.Firstly,combining the energy estimate and approximation procedure,we obtain the existence of the global solution.Secondly,the large deviation principle is obtained via the weak convergence method.
基金supported by the Soft Science Research Program of Science&Technology Department of Sichuan Province(2016ZR0097)
文摘Recently, the online social networks have emerged as one of the important platforms for social users. Among millions of users, famous person from entertainment circle arouse our interest. They promote social relationship and establish their reputation via these platforms. To analyze the social influence of entertainment stars we propose and implement a public cloud based framework to crawl celebrities' social messages from Sina Weibo, store the gathered messages and conduct various analysis to assess the socia influence. It consist of three key components: task generation, resource management and task scheduling, and influence analysis. The task generation is responsible of acquiring celebrities' socia accounts and issue crawling tasks. We propose a cross-media method to extract social accounts from webpages. The resource management and task scheduling will dynamic adjust the rented resource to minimize the total computing cost while keeping Qo S. We propose a dynamic instance provisioning strategy based on the large deviation principle. The influence analysis will undertake various types of analysis, such as fan count, posting frequency, textual analysis, and so on. More than 10,000 celebrities' microblogs have been gathered so far, and some related gainers, such as celebrities and ad agencies can gain the illumination brought by our analysis.
基金Supported by the LPMC at Nankai Universitythe NSF of China (Grant No. 10871103)
文摘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.
文摘This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems. We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology, while it does not satisfy the large deviation principles in the τ-topology.
基金supported by the National Natural Science Foundation of China under Grant No.12075016,No.11575016。
文摘From the perspective of Markovian piecewise deterministic processes(PDPs),we investigate the derivation of a kinetic uncertainty relation(KUR),which was originally proposed in Markovian open quantum systems.First,stationary distributions of classical PDPs are explicitly constructed.Then,a tilting method is used to derive a rate functional of large deviations.Finally,based on an improved approximation scheme,we recover the KUR.These classical results are directly extended to the open quantum systems.We use a driven two-level quantum system to exemplify the quantum results.
基金Supported by NSFC(Grant Nos.12171038,11871008)985 Projects。
文摘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.
基金supported by the National Science Foundation of China under Grants No. 11 174 025 and No. 11 575 016the support of the CAS Interdisciplinary Innovation Team, No. 2060 299。
文摘We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.
基金This work is partly supported by BJNSF(No.1212008)National Natural Science Foundation of China(No.11801032,12171032,11971227,12071123)Beijing Institute of Technology Research Fund Program for Young Scholars and Key Laboratory of Mathematical Theory and Computation in Information Security.
文摘In this paper,we establish a large deviation principle for two-dimensional primitive equations driven by multiplicative Lévy noises.The proof is based on the weak convergence approach.
