A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%...     

有向图上的随机游动

设G=(V,Г)是有向图,G上的随机游动X(G)定义如下:位于某个顶点上的一个粒子将以等概率转移到该顶点的所有后继顶点.令M(j,n)表示随机游动X(G)在前n步内访问顶点j的平均次数,用W(j)表示随机游动X(G)到达顶点j所需要的平均步效.我们对M(j,n)和W(j)的值进行了估计,证明了M(j,n)=O(n),并给出了W(j)的上界.     

The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

-混合序列的不变原理

给出一类较广泛的ρ-混合序列 ,并证明了在一定的矩条件下 ,ρ-混合序列的不变原理成立     

半直线上随机环境中的随机游动的常返性

本文讨论半直线上随机环境中的随机游动的常返性。在独立环境下，主要通过强大数定律，找到了非常返和正常返的一个充分条件下，并将这一结果推广到一些特殊情情形。在一般的随机环境下，主要通过数列的有界性，给出了常返与零常返的一个充分条件。     

Estimates for the Rapid Decay of Concentration Functions of n-Fold Convolutions

We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov–Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n ^–1/2). On the other hand, Esseen⁽³⁾ has shown that this rate is o(n ^–1/2) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.⁽⁹⁾ Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n ^–1/2).     

Analysis of nonlinear sliding structures by modified stochastic linearization methods

Probabilistic characteristics of a sliding structure is investigated by using new versions of stochastic linearization technique. The structure is composed of base part and upper part, which are connected to each other in a spring-damping system. Coulomb friction between the base structure and earth ground is considered. Two alternative versions of stochastic linearization approach, suggested by X. Zhang and I. Elishakoff, respectively, are applied to such a sliding structure to evaluate its statistical properties. Compared with the results of Monte Carlo simulation, the two new approaches are performing much better than the conventional one in their applications to the sliding structure. Moreover, numerical results indicate that the criterion proposed by Elishakoff turns out to be superior to all other versions in the problem under study. Numerical results also suggest that the entire structure may be replaced by the rigid body in the sliding problem as long as the difference of velocity responses are considered less important than those of displacement responses.     

Pulsed-Field-Gradient Measurements of Time-Dependent Gas Diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O₂, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 × 10⁻⁶m²s⁻¹for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times.