Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Max-Plus Stochastic Processes

This paper is concerned with processes which are max-plus counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. Concepts of max-plus martingale and max-plus stochastic differential equation are introduced. The max-plus counterparts of backward and forward PDEs for Markov diffusions turn out to be first-order PDEs of Hamilton–Jacobi–Bellman type. Max-plus additive integrals and a max-plus additive dynamic programming principle are considered. This leads to variational inequalities of Hamilton–Jacobi–Bellman type.     

钢球质量监测最佳抽检方案的确定

本文介绍概率抽样法在钢球生产过程中的应用,通过此法确定钢球生产中各工序质量监测的最佳抽检方案,以确保产品被接受的概率最大。     

Epi-Convergence and Lower and Epi-Upper Semicontinuous Approximations in Distribution

The paper introduces an extension of the epi-convergence, the lower semicontinuous approximation and the epi-upper semicontinuous approximation of random real functions in distribution. The new notions could be helpful tools for sensitivity analyzes of stochastic optimization problems. The research is evoked by S. Vogel and continues the research started by Vogel and the author.     

概率罐子模型中一种最优设计

基于错误概率达到最小的原则，该文在罐子模型序贯试验中构造了一种渐近最优设计。在这种设计下，不仅能使病员以较多机会分配到较好的处理，而且能使估计量的统计效率在一定意义下达到最优。     

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.     

Influence of relaxation effects on probabilities of the 2s2p35S2－2s22p2 3P1，2 intercombination transitions in NII

Transition probabilities of the 2s2p^3 {}^5S_2－2s^22p^2 {}^3P_{1,2} intercombination transitions in NII have been calculated by using a large-scale multiconfiguration Dirac－Fock method. In the calculation the most important effects of relativity, correlation, and relaxation are considered. From the calculated transition probabilities, the lifetime of the 2s2p^3 {}^5S_2 metastable state is derived. The result is in excellent agreement with the latest experimental result. In the meantime the influence of anomalously strong relaxation effects on probabilities of the 2s2p^3 {}^5S_2－2s^22p^2 {}^3P_{1,2} lines in NII have been found.     

Optimal volume-corrected laplace-metropolis method

The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccioet al. The correction volume of probability α in DiCiccioet al. is fixed and suggested to take the value α=0.05. In this article α is selected based on an asymptotic analysis to minimize the mean square relative error (MSRE). This optimal choice of α is shown to be invariant under linear transformations. The invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical use. A simulation study and a real data example are presented.     

保险公司离散型崩溃模型研究

本文提出并讨论了含投资因素、红利分配因素的崩溃模型，得出了关于崩溃概率、保险公司的期望寿命的结论，这些结论推广了没有考虑投资因素的崩溃模型的相关结论．     

Simple Constructions of Almost k-wise Independent Random Variables

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity.