On the central limit theorem for the stationary Poisson process of compact sets

Stochastic geometry models based on a stationary Poisson point process of compact subsets of the Euclidean space are examined. Random measures on ?^d, derived from these processes using Hausdorff and projection measures are studied. The central limit theorem is formulated in a way which enables comparison of the various estimators of the intensity of the produced random measures. Approximate confidence intervals for the intensity are constructed. Their use is demonstrated in an example of length intensity estimation for the segment processes. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral analysis of the covariance of the almost periodically correlated processes

This paper deals with the spectrum of the almost periodically correlated (APC) processes defined on . It is established that the covariance kernel of such a process admits a Fourier series decomposition, K(s+t, s) , whose coefficient functions b are the Fourier transforms of complex measures m, , which are absolutely continuous with respect to the measure m_o. Considering the APC strongly harmonizable processes, the spectral covariance of the process can be expressed in terms of these complex measures m.

The usual estimators for the second order situation can be modified to provide consistent estimators of the coefficient functions b from a sample of the process. Whenever the measures m are absolutely continuous with respect to the Lebesgue measure, so m(dλ)=f(λ) dλ, the estimation of the corresponding density functions f is considered. Under hypotheses on the covariance kernel K and on the coefficient functions b, we establish rates of convergence in quadratic mean and almost everywhere of these estimators.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

基于残差图像的迭代终止条件及其在NCSR算法中的应用

现有图像去模糊(deblurring)算法多依赖于 正则化技术以迭代逼近求解最优目标函数 方式实现关于原图像的最佳估计,由于缺乏迭代终止判定条件(ITC),这些算法通常采用固 定迭代 次数实现以至执行效率不高,同时所获得图像的质量在很多时候也未必是最佳的。鉴于在迭 代过程中每一步所获得的中间估计图像经与模糊核卷积后和模糊图像之间残差图像的亮度 值具有显著的高斯分布特点,提出使用广义高斯分布(GGD)模型为迭代过程中的残差图像建 模并以GGD模型参数值作为衡量去模糊效果的度量 (DM,deblurring measure)。基于DM,在保障去模糊图像质量的前提下,设计了ITC自适应 地终止迭代过程以提高去模糊算法的计算 效率。在经典的非局部集中稀疏表示(NCSR,nonlocally centralized sparse representat ion)去模糊算法上完成的大量 的实验表明,对于运动、高斯和失焦3种典型的模糊失真,新提出的ITC能 够有效判定在每一步迭代过程中所获得的估计图像是否已达到最佳的图像质量,从而实现 在保障去模糊图像质量的前提下大幅度提高NCSR算法计算效率的目的。所提出的ITC判定方 法具有普适性,调整相关参数后也可以应用于其它迭代型的去模糊算法。     

Zeros of the densities of infinitely divisible measures on R n

Let be an infinitely divisible probability measure onR ⁿ without Gaussian component and let be its Lévy measure. Suppose that is absolutely continuous with respect to the Lebesgue measure . We investigate the structure of the set ⁿ of admissible translates of . This yields a unified presentation of previously known results. We also show that if(S)>0 then is equivalent to , under the assumption that supp =R ⁿ , whereS is the closure of the semigroup generated by the support of .The research of this author is supported by KBN Grant.The research of this author is supported by AFSOR Grant No. 90-0168, and the University of Tennessee Science Alliance, a State of Tennessee Center of Excellence.     

M/G/∞ with alternating renewal breakdowns

We consider an M/G/ queue where the service station is subject to occasional interruptions which form an alternating renewal process ofup anddown periods. We show that under some natural conditions the random measure process associated with the residual service times of the customers is regenerative in the strict sense, and study its steady state characteristics. In particular we show that the steady state distribution of this random measure is a convolution of two distributions of (independent) random measures, one of which is associated with a standard M/G/ queue.     

Packing measure of the sample paths of fractional Brownian motion

Let be a fractional Brownian motion of index in If , then there exists a positive finite constant such that with probability 1,

where and - is the -packing measure of .

     

On transversely flat conformal foliations with good measures

Transversely flat conformal foliations with good transverse invariant measures are Riemannian in the sense. In particular, transversely similar foliations with good measures are transversely Riemannian as transversely -foliations.

     

An Example on the Controllability of Perturbed Linear Control Systems

We show by an example that small perturbations with respect to the convergence in measure of the coefficients A and B may affect the complete controllability of the linear control system , where x is the state and u is the control. This answers a question raised in Ref. 1.     

Grand canonical distribution for multicomponent system in the collective variables method

The collective variables method with a reference system is developed for the case of the grand canonical ensemble for a multicomponent continuous system. The method is used to investigate phase transitions in a binary system. For a binary symmetrical system the relations between microscopic parameters determining the alternation of gas-liquid and separation phase transitions are found. The functional of the grand partition function of the symmetrical mixture is examined in the framework of parameters containing the separation point. The system is described with two sets of collective variables: _k, a set connected with the gas-liquid critical point, andc _k, a set connected with the separation phenomenon. The fourfold basic density measure is constructed inc _k-variable phase space which contains the variablec _v connected with the order parameter of the system. It is shown that the problem can be reduced to the 3D Ising model in an external field.