A Continuous Super-Brownian Motion in a Super-Brownian Medium

A continuous super-Brownian motion is constructed in which branching occurs only in the presence of catalysts which evolve themselves as a continuous super-Brownian motion . More precisely, the collision local time (in the sense of Barlow et al. ⁽¹⁾) of an underlying Brownian motion path W with the catalytic mass process goerns the branching (in the sense of Dynkin's additive functional approach). In the one-dimensional case, a new type of limit behavior is encountered: The total mass process converges to a limit without loss of expectation mass (persistence) and with a nonzero limiting variance, whereas starting with a Lebesgue measure , stochastic convergence to occurs.     

A Class of Affine Processes Arising as Fluctuation Limits of Super-Brownian Motion in a Super-Brownian Catalytic Medium

A class of infinite dimensional Ornstein-Uhlenbeck processes that arise as solutions of stochastic partial differential equations with noise generated by measure-valued catalytic processes is investigated. It will be shown that the catalytic Ornstein-Uhlenbeck process with super-Brownian catalyst in one dimension arises as a high density fluctuation limit of a super-Brownian motion in a super-Brownian catalyst with immigration. The main tools include Laplace transformations of stochastic processes, analysis of a non-linear partial differential equation and techniques on continuity and regularity based on properties of the Sobolev spaces.     

Intersection Local Time for Two Independent Fractional Brownian Motions

Let B ^H and be two independent, d-dimensional fractional Brownian motions with Hurst parameter H∈(0,1). Assume d≥2. We prove that the intersection local time of B ^H and

Super-Brownian motion: Path properties and hitting probabilities

Summary Sample path properties of super-Brownian motion including a one-sided modulus of continuity and exact Hausdorff measure function of the range and closed support are obtained. Analytic estimates for the probability of hitting balls lead to upper bounds on the Hausdorff measure of the set of k-multiple points and a sufficient condition for a set to be polar.Dedicated to Klaus Krickeberg on the occasion of his 60th birthdayResearch partially supported by a Natural Sciences and Engineering Research Council of Canada operating grant     

A Special Integral Representation for a Local Residue

We obtain a new integral representation for a local residue with integration of a meromorphic m ²-form over an m ²-dimensional cycle in .     

垂直密度表示及其应用

该文论述了Vertical Density Representation (VDR)的历史发展, 现状及其在随机数生成, 多元密度构造等领域的应用及在非正态多元统计分析的潜在应用.     

Representation of Continuous Functions and Its Applications

In this work, we introduce a Representation of continuous real-valued functions defined over a real Hilbert space. As a consequence, we can introduce a Sandwich Theorem for semi-continuous functions, a Separation Theorem for closed sets and a representation Theorem of lower semi-continuous functions.     

Pathwise Convergence of a Rescaled Super-Brownian Catalyst Reactant Process

Consider the one-dimensional catalytic super-Brownian motion X (called the reactant) in the catalytic medium which is an autonomous classical super-Brownian motion. We characterize both in terms of a martingale problem and (in dimension one) as solution of a certain stochastic partial differential equation. The focus of this paper is for dimension one the analysis of the longtime behavior via a mass-time-space rescaling. When scaling time by a factor of K, space is scaled by K ^η and mass by K ^−η. We show that for every parameter value η ≥ 0 the rescaled processes converge as K→ ∞ in path space. While the catalyst’s limiting process exhibits a phase transition at η = 1, the reactant’s limit is always the same degenerate process.      

Hilbert-Space-Valued Super-Brownian Motion and Related Evolution Equations

A stochastic partial differential equation in which the square root of the solution appears as the diffusion coefficient is studied as a particular case of stochastic evolution equations. Weak existence of a solution is proved by the Euler approximation scheme. The super-Brownian motion on [0, 1] is also studied as a Hilbert-space-valued equation. In this set up, weak existence, pathwise uniqueness, and positivity of solutions are obtained in any dimension d . Accepted 23 October 1998     

“Two Nontrivial Critical Points for Nonsmooth Functionals via Local Linking and Applications”

In this paper, we extend to nonsmooth locally Lipschitz functionals the multiplicity result of Brezis–Nirenberg (Communication Pure Applied Mathematics and 44 (1991)) based on a local linking condition. Our approach is based on the nonsmooth critical point theory for locally Lipschitz functions which uses the Clarke subdifferential. We present two applications. This first concerns periodic systems driven by the ordinary vector p-Laplacian. The second concerns elliptic equations at resonance driven by the partial p-Laplacian with Dirichlet boundary condition. In both cases the potential function is nonsmooth, locally Lipschitz.     

Cayley-Hamilton定理的两种简单证法和两个表现定理

本文对Cayley-Hamilton定理提出两种简单证法并应用该定理和罗必塔法则给出两个有关二阶张量函数的表现定理.     

结构矩阵的三角表示及其应用

利用位移铁和交换Hessenberg矩阵代数给出结构矩阵的三角表示,并讨论在Toeplitz矩阵和Toeplitz Hankel矩阵方面的应用。     

A Compact Representation for Modular Semilattices and Its Applications

Order - A modular semilattice is a semilattice generalization of a modular lattice. We establish a Birkhoff-type representation theorem for modular semilattices, which says that every modular...     

关于模糊复数的两个表现定理

给出模糊复数的两个表现定理。     

稀疏表示及其在人脸识别中的应用

稀疏表示是近年来新兴的一种数据表示方法,是对人类大脑皮层编码机制的模拟。稀疏表示以其良好的鲁棒性、抗干扰能力、可解释性和判别性等优势,广泛应用于模式识别领域。基于稀疏表示的分类器在人脸识别领域取得了令人惊喜的成就,它将训练样本看成字典,寻求测试样本在字典下的最稀疏的表示,即用尽可能少的训练样本的线性组合来重构测试样本。但是经典的基于稀疏表示的分类器没有考虑训练样本的类别信息,以致被选中的训练样本来自许多类,不利于分类,因此基于组稀疏的分类器被提出。组稀疏方法考虑了训练样本的类别相似性,其目的是用尽可能少类别的训练样本来表示测试样本,然而这类方法的缺点是同类的训练样本或者同时被选中或者同时被丢弃。在实际中,人脸受到光照、表情、姿势甚至遮挡等因素的影响,样本之间关系比较复杂,因此最后介绍局部加权组结构稀疏表示方法。该方法尽量用来自于与测试样本相似的类的训练样本和来自测试样本邻域的训练样本来表示测试样本,以减轻不相关类的干扰,并使得表示更稀疏和更具判别性。     

两个数学模型及其应用

给出了两个数学模型,模型Ⅰ—教学编制模型,模型Ⅱ—课时津贴模型,并结合实际问题进行了计算     

Birth and Death on a Flow: Local Time and Estimation of a Position‐Dependent Death Rate

The paper deals with statistical inference for an unknown rate of position‐dependent killing in birth and death on a flow. We introduce local time for this process and discuss its asymptotics with the help of a Tanaka formula. As a consequence, we can prove asymptotic normality of kernel estimators for the death rate. This revised version was published online in June 2006 with corrections to the Cover Date.     

Representation of a Class of Linear Operators with Coupled Domain in a Product Space and Its Applications

Acta Mathematica Sinica, English Series - This paper is concerned with the representation problem of a coupled operator in a product space. A necessary and sufficient condition is given for a class...