Stable Manifolds and Nonuniform Hyperbolicity: Optimal Estimates

We establish the existence of invariant stable manifolds for C ¹ perturbations of a nonuniform exponential dichotomy with an arbitrary nonuniform part. We consider the general case of sequences of maps, which corresponds to a nonautonomous dynamics with discrete time. We also obtain optimal estimates for the decay of trajectories along the stable manifolds. The optimal C ¹ smoothness of the invariant manifolds is obtained using an invariant family of cones.     

Generalized Pseudo-Likelihood Estimates for Markov Random Fields on Lattice

In this paper we generalize Besag's pseudo-likelihood function for spatial statistical models on a region of a lattice. The correspondingly defined maximum generalized pseudo-likelihood estimates (MGPLEs) are natural extensions of Besag's maximum pseudo-likelihood estimate (MPLE). The MGPLEs connect the MPLE and the maximum likelihood estimate. We carry out experimental calculations of the MGPLEs for spatial processes on the lattice. These simulation results clearly show better performances of the MGPLEs than the MPLE, and the performances of differently defined MGPLEs are compared. These are also illustrated by the application to two real data sets.     

局部熵高维重分形谱的上界估计

We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.     

Harmonizable stable processes on groups: spectral,ergodic and interpolation properties

Summary This work extends to symmetric -stable (SS) processes, 1<<2, which are Fourier transforms of independently scattered random measures on locally compact Abelian groups, some of the basic results known for processes with finite second moments and for Gaussian processes. Analytic conditions for subordination of left (right) stationarily related processes and a weak law of large numbers are obtained. The main results deal with the interpolation problem. Characterization of minimal and interpolable processes on discrete groups are derived. Also formulas for the interpolator and the corresponding interpolation error are given. This yields a solution of the interpolation problem for the considered class of stable processes in this general setting.Research supported by AFOSR contract F49620 82 C0009On leave from the Institute of Mathematics, Technical University 50-370 Wrocaw, Poland     

Estimates for the Upper Bounds of the First Eigenvalue on Submanifolds

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Estimates on the Transition Densities of Girsanov Transforms of Symmetric Stable Processes

In this paper, we first study a purely discontinuous Girsanov transform which is more general than that studied in Chen and Song [(2003), J. Funct. Anal. 201, 262–281]. Then we show that the transition density of any purely discontinuous Girsanov transform of a symmetric stable process is comparable to the transition density of the symmetric stable process. The same is true for the Girsanov transform introduced in Chen and Zhang [(2002), Ann. Inst. Henri poincaré 38, 475–505]. As an application of these results, we show that the Green function of Feynman–Kac type transforms of symmetric stable processes by continuous additive functionals of zero energy, when exists, is comparable to that of the symmetric stable process.      

Reflected Brownian Motion in a Convex Polyhedral Cone: Tail Estimates for the Stationary Distribution

Consider a multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this distribution at an exponential rate, as time goes to infinity, complementing the results of Dupuis and Williams (Ann Probab 22(2):680–702, 1994) and Atar et al. (Ann Probab 29(2):979–1000, 2001). We also prove that certain exponential moments for this distribution are finite, thus providing a tail estimate for this distribution. Finally, we apply these results to systems of rank-based competing Brownian particles, introduced in Banner et al. (Ann Appl Probab 15(4):2296–2330, 2005).     

E^n+1中闭超曲面上λ_1^r^L的上界估计

本文研究E^n＋1的中闭超曲面上的Lr（0≤r≤n）算子，得到其第一非零特征值心的两个上界估计，改进和推广了Alias等人的相应结论。     

Curvature Estimates for Strongly Stable Domains on Surfaces with Constant Mean Curvature in Space Forms

ＣｕｒｖａｔｕｒｅＥｓｔｉｍａｔｅｓｆｏｒＳｔｒｏｎｇｌｙＳｔａｂｌｅＤｏｍａｉｎｓｏｎＳｕｒｆａｃｅｓｗｉｔｈＣｏｎｓｔａｎｔＭｅａｎＣｕｒｖａｔｕｒｅｉｎＳｐａｃｅＦｏｒｍｓ（ＷａｎｇＺｈｉｇｕｏ）；（王治国）（ＷｕＺｈｉｑｉｎｇ）；（吴志勤）（...     

关于非协调Qrot1元可计算上界后验误差估计的一个注记

通过数值试验发现Ainsworth建立的非协调Qrot1元可计算上界后误差估计指示子的可靠、有效性差.参照相关文献以及根据Qrot1元的性质,在Ainsworth建立的可计算上界后验误差估计框架下对插值后处理函数的构造和选取分别作了修改和更换,并相应获得可靠且有效的可计算上界后验误差估计,给出了三个不同类型的例子及其实验结果.     

Path Boxplots: A Method for Characterizing Uncertainty in Path Ensembles on a Graph

Graphs are powerful and versatile data structures that can be used to represent a wide range of different types of information. In this article, we introduce a method to analyze and then visualize an important class of data described over a graph—namely, ensembles of paths. Analysis of such path ensembles is useful in a variety of applications, in diverse fields such as transportation, computer networks, and molecular dynamics. The proposed method generalizes the concept of band depth to an ensemble of paths on a graph, which provides a center-outward ordering on the paths. This ordering is, in turn, used to construct a generalization of the conventional boxplot or whisker plot, called a path boxplot, which applies to paths on a graph. The utility of path boxplot is demonstrated for several examples of path ensembles including paths defined over computer networks and roads. Supplementary materials for this article are available online.     

Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction

Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of potential theory and rational approximation theory. The study of the asymptotic behavior of the roots of these polynomials reveals a surprisingly rich geometry, which reflects three characteristics: the relative position of an island in the archipelago, the analytic continuation picture of the Schwarz function of every individual boundary and the singular points of the exterior Green function. By way of explicit example, fine asymptotics are obtained for the lemniscate archipelago |z^m−1|<r^m, 0<r<1, which consists of m islands. The asymptotic analysis of the Christoffel functions associated to the same orthogonal polynomials leads to a very accurate reconstruction algorithm of the shape of the archipelago, knowing only finitely many of its power moments. This work naturally complements a 1969 study by H. Widom of Szegő orthogonal polynomials on an archipelago and the more recent asymptotic analysis of Bergman orthogonal polynomials unveiled by the last two authors and their collaborators.     

Stable properties of plethysm : on two conjectures of Foulkes

Two conjectures made by II.O. Foulkes in 1950 can be stated as follows.

Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times

Every birth and death chain on a finite tree can be represented as a random walk on the underlying tree endowed with appropriate conductances. We provide an algorithm that finds these conductances in linear time. Then, using the electric network approach, we find the values for the stationary distribution and for the expected hitting times between any two vertices in the tree. We show that our algorithms improve classical procedures: they do not exhibit ill-posedness and the orders of their complexities are smaller than those of traditional algorithms found in the literature.     

Quasi-Invariance of the Wiener Measure on Path Spaces: Noncompact Case

For a geometrically and stochastically complete, noncompact Riemannian manifold, we show that the flows on the path space generated by the Cameron-Martin vector fields exist as a set of random variables. Furthermore, if the Ricci curvature grows at most linearly, then the Wiener measure (the law of Brownian motion on the manifold) is quasi-invariant under these flows.     

Upper estimates for hyperbolic metrics on subdomains: the case of equality

It is the purpose of this paper to supplement our previous work concerning upper estimates for hyperbolic metrics on subdomains. Specifically, our interest is in determining when equality holds in the relevant inequality to clarify the situation that has failed to be explicitly mentioned before. The method of proof again involves a standard technique based on the classical Schwarz–Pick lemma.     

Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra I: A Priori Estimates

ABSTRACT

Let 𝒯 _k be a sequence of triangulations of a polyhedron Ω ? ? ⁿ and let S _k be the associated finite element space of continuous, piecewise polynomials of degree m. Let u _k  ∈ S _k be the finite element approximation of the solution u of a second-order, strongly elliptic system Pu = f with zero Dirichlet boundary conditions. We show that a weak approximation property of the sequence S _k ensures optimal rates of convergence for the sequence u _k . The method relies on certain a priori estimates in weighted Sobolev spaces for the system Pu = 0 that we establish. The weight is the distance to the set of singular boundary points. We obtain similar results for the Poisson problem with mixed Dirichlet–Neumann boundary conditions on a polygon.     

收入对居民消费影响的结构性路径分析:江苏案例

基于社会核算矩阵(SAM)和SAM结构性路径分析模型,以江苏为例,研究扩大居民消费需求的路径选择问题.主要研究结论:第一,增加收入的确可以实现扩大内需的目标,但是,对不同行业的效果存在很大差异.其中,对食品消费相关产业与居住消费相关的产业影响较大;第二,影响商品(服务)消费需求变动主要是直接相关行业,而传导机制主要依赖于传导速度较快的直接路径,但效果并非最好;第三,提高农村居民收入水平更能有效地拉动居住和交通通讯消费产业的经济效益,而文教娱乐消费行业经济效益的提高更主要是依赖于城镇居民消费需求的变动;第四,农村应将投资重点放在信息化、公共基础设施等方面,城镇应将投资重点放在服务业以及消费转化效应较大的科技、教育、文化、卫生等社会事业领域.