Continuity and Representation of Gaussian Mehler Semigroups

We present sufficient conditions on a Gaussian Mehler semigroup on a reflexive Banach space Eto be induced by a single positive symmetric operator Q \in , and give a counterexample which shows that this representation theorem is false in every nonreflexive Banach space with a Schauder basis. We also show that the transition semigroup of a Gaussian Mehler semigroup on a separable Banach space Eacts in a pointwise continuous way, uniformly on compact subsets of E, in the space BUC(E) of bounded uniformly continuous real-valued funtions on E. The transition semigroup is shown to be strongly continuous on BUC(E) if and only if S(t) = Ifor all t 0     

Representation of Gaussian isotropic spin random fields

We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin line bundles of the 2$2$-sphere. In particular, every complex Gaussian isotropic spin random field can be represented in this way. Our construction extends P. Lévy’s original idea for the spherical Brownian motion.     

A Spectral Representation for Bounded Non-Selfadjoint Operators

An integral representation for an arbitrary bounded operator T defined on a Hilbert space ${\mathcal{H}}$ is given. The representing measure is in general defined on a Jordan curve surrounding the spectrum of T. It is obtained as a limit, in a certain weak sense, of a family (F _r ) of absolutely continuous measures the Radon?CNikodym derivative of which (with respect to the standard Lebesgue measure on the considered Jordan curve) are described explicitly in terms of the operator T and its adjoint T ^*.     

Some Self-Adjoint Quantum Semimartingales

It is proved that the quantum stochastic gauge integral preservesself-adjointness of vacuum-adapted processes. This fact, togetherwith bounded perturbations and the link between the Hudson–Parthasarathycalculus and vacuum-adapted theory, is used to produce manyself-adjoint quantum semimartingales. 2000 Mathematics SubjectClassification 81S25, 47D06, 47A56.     

On the Representation of Functions with Gaussian Wave Packets

We introduce Gaussian wave packets in pursuit of representations of functions, in which the representation is invariant under translation, modulation, scale, rotation and anisotropic dilation. Properties of both continuous and discrete representations are discussed. For the discrete (two-dimensional) case, we develop fast algorithms for the application of the analysis and synthesis operators. A main objective for using Gaussian wave packets is to obtain sparse approximations of functions. However, due to the many invariance properties, the representations will have a high degree of redundancy. Therefore, we also introduce sparse methods for highly redundant representations, that employ some of the analytic properties of Gaussian wave packet for gaining computational efficiency.     

On the Spectral Distribution of Gaussian Random Matrices

We consider the empirical spectral distribution （ESD） of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotaeh approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O（n^-1） to the Wigner distribution function uniformly on every compact intervals [u,v] within the limiting support （-1, 1）. Furthermore, the variance of the ESD for such an interval is proved to be （πn）^-2 logn asymptotically which surprisingly enough, does not depend on the details （e.g. length or location） of the interval, This property allows us to determine completely the covariance function between the values of the ESD on two intervals.     

Semimartingales from the Fokker-Planck Equation

We show the existence of a semimartingale of which one-dimensional marginal distributions are given by the solution of the Fokker-Planck equation with the pth integrable drift vector (p > 1).     

Clark Representation for Local Times of Self-Intersection of Gaussian Integrators

Ukrainian Mathematical Journal - We prove the existence of multiple local times of self-intersection for a class of Gaussian integrators generated by operators with finite-dimensional kernels,,...     

Spectral properties of processes derived from stationary Gaussian sequences

Many qualitative properties of the spectral measure of a stationary Gaussian sequence are spectral properties of the underlying shift transformation. This has implications in time series analysis.     

非平稳随机过程模拟的一个谱表示方法

本文由Priestley渐进谱理论导出了非平稳随机过程蒙特卡罗模拟的一个谱表示方法.按照该方法,样本过程可直接由一余弦级数公式计算产生.可以证明,当级数项数足够大时,模拟的样本过程可准确地反映非平稳随机过程规定的性质;当产生的样本过程足够多时,其总体均值和总体自相关函数均趋于相应目标函数;样本过程随着级数项数趋于无穷而渐近呈正态分布.本文方法最显著的特点在于可以借助随机相位角产生具有某些预期特征的样本过程.     

Semimartingales and geometric inequalities on manifolds

The purpose of this paper is twofold. First, we use resultson Jacobi fields to study the stochastic differential equations(SDEs) for exp_Xt( exp_Xt^-1(Y_t)) with specially constructed coupledsemimartingales X and Y on a complete, simply connected Riemannianmanifold M with constant sectional curvature. Secondly, we applythese SDEs to obtain an analogue for M of a result of Borellconcerning an inequality relating the solutions of the parabolicequation / t = 1/2 – h, with Dirichlet boundary condition,on three convex sets in Euclidean space. From the latter, therefollows an inequality involving the first eigenvalues of theLaplacian on those convex sets with the Dirichlet boundary condition,analogous to an inequality in Euclidean space which is equivalentto the Brunn–Minkowski inequality of these eigenvaluesobtained by Brascamp and Lieb.     

Arrow-Mangasarian Sufficient Conditions for Controlled Semimartingales

Abstract

This article shows a version of Arrow's generalization of Manga-sarian's sufficient conditions valid for controlled stochastic differential equations driven by semimartingales. The infinite horizon case is covered. An example is given.     

Remarks on a Noncanonical Representation for a Stationary Gaussian Process

For a stationary centered Gaussian process, we construct a noncanonical representation which has an infinite-dimensional orthogonal complement that is nontrivial. The authors have already proposed a systematic method for the construction of noncanonical representation having a finite-dimensional orthogonal complement.     

Spectral analysis of certain compact factors for Gaussian dynamical systems

For factors of a Gaussian automorphismT determined by compact subgroups of the group of unitary operators acting onL ² of the spectral measure ofT, we prove that the maximal spectral multiplicity is either 1 or infinity. As an application, we show that the maximal multiplicity of those factors an allL ^p, 1<p<+∞, is the same.     

半鞅及其临界停时

本文讨论Ｂ－值Ｒ．Ｒ．Ｃ过程Ｗ的半鞅性及其与临界停时之间的关系，同时给出相应的临界停时的构作方法，并证明过程Ｗ为非半鞅的特征为Ｐ（＜∞）＞０．本文最后讨论两类矢值过程，它们具有一个Ｒ－控制过程，但不为半鞅．     

特殊半鞅的一个局部性质

本文讨论特殊半鞅的一个局部性质,将局部（平方可积）鞅的结果推广到了一类特殊半鞅的情形。     

Some Generalizations of Semimartingales in the Plane

51.IntroductionTwo(parametersemi-martingaleswereinvestigated,forexample,inthepaperbyBrennan[21,Cairoli[3]andZakai[81.Inthispaperwegeneralizetheconceptofatwo-parametersemimartingaleandinvestigatesomepropertiesofthegeneralizedsemi-martingaoes.Wealsodefineaclassofpositivemeasuresassociatedwiththegeneralizedsemi-martingales.InSectionII,followingtheterminologygivenin[21,wedefinestrongandweakA--processesoforderp,alsofor15p相似文献