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 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.

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.

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.

Influence Analysis for Celebrities via Public Cloud and Social Platform

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.

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].

Uniform Asymptotics for Finite-Time Ruin Probabilities of Risk Models with Non-Stationary Arrivals and Strongly Subexponential Claim Sizes

This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim sizes.Further,as an application of the result of onedimensional risk model,we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.

Deriving a kinetic uncertainty relation for piecewise deterministic processes:from classical to quantum

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.

Counting single cells and computing their heterogeneity:from phenotypic frequencies to mean value of a quantitative biomarker

This tutorial presents a mathematical theory that relates the probability of sample frequencies,of M phenotypes in an isogenic population of N cells,to the probability distribution of the sample mean of a quantitative biomarker,when the N is very large.An analogue to the statistical mechanics of canonical ensemble is discussed.

A fluctuation theorem for Floquet quantum master equations

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.

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.