A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY 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).

Large Deviation Principle for a Form of Compound Nonhomogeneous Poisson Process

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.

Unified Limits and Large Deviation Principles forβ-Laguerre Ensembles in Global Regime

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.

Large Deviation Principle for the Two-dimensional Stochastic Navier-Stokes Equations with Anisotropic Viscosity

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.

Large Deviation Principle for the Fourth-order Stochastic Heat Equations with Fractional Noises

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.

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

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.

Large deviation principle for diffusion processes under a sublinear expectation

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.

On Uniform Large Deviations Principle for Multi-valued SDEs via the Viscosity Solution Approach

This paper deals with the uniform large deviations for multivalued stochastic differential equations(MSDEs for short) by applying a stability result of the viscosity solutions of second order Hamilton-Jacobi-Belleman equations with multivalued operators.Moreover, the large deviation principle is uniform in time and in starting point.

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

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.

On Small Time Large Deviation Principle for Diffusion Processes on Hilbert Spaces under Non-Lipschitzian Condition

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.

Large deviation principle of stochastic differential equations with non-Lipschitzian coefficients

我们与 non-Lipschitzian 和非同类的系数学习随机的微分方程的大偏差原则。当系数和 b 被围住时，我们起初考虑大偏差原则，然后，我们由使用围住的近似节目概括结论到无界的大小写。我们的结果是 S 的归纳。Fang-T。Zhangs 结果。

Large deviation principles for stationary NA sequences

Under general conditions, the large deviation principles for partial sums of stationary NA sequences are proved.

Limit Theorems and Large Deviations forβ-Jacobi Ensembles at Scaling Temperatures

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.

柏拉图–伽马模型下尾在险价值度量的贝叶斯估计的渐近行为及其应用

针对柏拉图–伽马风险模型的尾在险价值度量的贝叶斯估计量的渐近行为进行研究有助于对风险度量进行统计推断,以便于风险投资者及时采取相应措施规避风险。首先,通过构造柏拉图–伽马模型的贝叶斯假设,给出了尾在险价值度量的贝叶斯估计量,并利用经典的大偏差和中偏差理论,以及Delta方法得到了尾在险价值度量的贝叶斯估计量的渐近行为,包括渐近正态性、大偏差原理和中偏差原理;其次,给出了尾在险价值度量的贝叶斯估计量的中偏差原理在统计假设检验方面的具体应用,得到了第一类错误和势函数的渐近行为;最后,通过数值模拟的方法,计算并模拟了尾在险价值的置信区间及其区间覆盖率,并在不同样本容量下画出了尾在险价值度量的贝叶斯估计量标准化后的直方图和核密度估计曲线,这与标准正态分布密度函数曲线基本重合,从而验证了估计量的渐近正态性,同时还模拟了尾在险价值度量的贝叶斯估计量相关的尾概率,模拟结果表明样本容量充分大时,尾概率以一定的速度趋近于零,由此验证了估计量的中偏差原理。

噪声驱动的随机Cahn-Hilliard方程的大偏差原理

研究了时间分式空间有色噪声驱动的随机Cahn-Hilliard方程解的存在性和唯一性。利用截断函数处理漂移项,利用变量替换处理随机积分,得到了局部解;验证了局部解的弱收敛性,获得了原方程温和解与Hurst指数之间的关系;验证了方程在特殊噪声下骨架函数的正则性,得到了Freidlin-Wentzell关系式。最后验证了大偏差原理。

Large Deviation for Stochastic Cahn-Hilliard Partial Differential Equations

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.

Large deviations for Glauber dynamics of continuous gas

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 T-topology.

Large Deviations for 2D Primitive Equations Driven by Multiplicative Lévy Noises

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.

SIMPLE PROOF OF A LARGE DEVIATION RESULT

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

基于大偏差原理的多维偏差源扰动下装配精度保持性分析方法

针对航空复杂产品装配过程中,多维装配偏差源间的非线性耦合作用会导致装配精度传递保持能力弱且可能发生极大装配超差的现象,提出一种基于概率法的装配过程精度保持性评价模型与方法。首先,分析装配偏差引起的应力作用,研究基于应力效应的多维装配偏差耦合聚焦超差效应,并以概率评价法为基础研究装配精度保持性;其次,采用大偏差原理中Gartner-Ellis定理分析装配过程极大超差问题的发生概率,建立融合偏差分析与大偏差原理的装配精度保持性评价概率模型;此后,利用动态滑动窗口法实现基于实测信息的超差概率计算,并以此结果为判据提出装配精度保持性的反馈调整措施。以某典型机翼盒段件为例,通过计算装配过程外形对缝间隙与阶差指标发生极大超差的概率,并借助装配超差预防优化系统实现装配过程的精确调整,提升装配质量约30%,增强了装配过程精度处于受控范围的能力。