Geostochastic calculus

A stochastic calculus for a family of continuous measure-valued Markov processes is developed. Such processes arise naturally in the construction of stochastic models of spatially distributed populations. The stochastic calculus is a tool whereby a class of density-dependent models can be studied in terms of the multiplicative measure diffusion process. In this paper the stochastic integral is introduced in the space-time setting and a Cameron-Martin-Girsanov theorem is established.     

Some aspects of modern population mathematics

The purpose of this paper is to survey a number of the technical tools and models that have found use in the study of human and other populations, and to indicate some problems of current interest. These tools and models are varied: integral equations, nonlinear oscillations, differential geometry, dynamical systems, nonlinear operations, bifurcation theory, semigroup theory, martingale theory, Markov processes, diffusion processes, branching processes, ergodic theory, prediction theory and state-space models. A fairly extensive bibliography is provided. Also an Appendix has been added describing the analysis of a classical entomological data set.     

Length-Biassed Sampling from a Finite Population

Expressions are derived for the interval moments of a length-biassed sample from a renewal process of finite length.     

过程工业故障诊断知识描述及形式化

本文根据智能工程技术，在开发过程工业集成化智能诊断软件系统的实践中，通过对过程工业故障诊断共性的分析，提出了过程工业故障诊断知识描述及形式化，研究了化工过程故障诊断浅知识模型和深知识模型的集成机制，以化工过程为例，用ＩＩＦＤＳ提供的面向对象知识表达方法，实现了一个诊断系统。     

The weighted sequential likelihood ratio

Strong approximation of the maximum-likelihood-ratio statistic by a diffusion process is given. This allows one to develop statistics using different weight functions. Sequential tests obtained include the ones earlier defined by Barbour (1979). The precision of the approximations is examined.     

Approximation spline de la prevision d'un processus fonctionnel autorégressif d'ordre 1

ABSTRACT We present a method to approximate and forecast, on an entire interval, a continuous-time process. For this purpose, we use the modelization of ARH(l) processes, defined by Bosq (1991). We deal with the practical problem of the discretization of the observed trajectories and approximate them by means of spline functions. We show by simulations that for well-chosen smoothing parameters, good prediction can be obtained in comparison with the “predictable” part of the process. Finally, we apply this model to forecast road traffic and compare it with a SARIMA model.     

层次分析法（AHP）在选择教材中的应用

选择教材是一个多目标决策问题．萨蒂的层次分析法提供了解决这类问题的一个方法．本文简要地介绍了层次分析法，并将其应用于数学教材的优选．     

Goodness of fit for the inverse Gaussian distribution

For testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution-function statistic A² is studied. Two procedures are followed in constructing the test statistic; they yield the same asymptotic distribution. In the first procedure the parameters in the distribution function are directly estimated, and in the second the distribution function is estimated by its Rao-Blackwell distribution estimator. A table is given for the asymptotic critical points of A². These are shown to depend only on the ratio of the unknown parameters. An analysis is provided of the effect of estimating the ratio to enter the table for A². This analysis enables the proposal of the complete operating procedure, which is sustained by a Monte Carlo study.     

Moderate Deviations for Bayes Posteriors

Let ( X_k ) k be a sequence of i.i.d. random variables taking values in a set , and consider the problem of estimating the law of X₁ in a Bayesian framework. We prove, under mild conditions on the prior, that the sequence of posterior distributions satisfies a moderate deviation principle.     

中国古代戏剧源流新论

中国古代戏剧的源流问题一直是戏剧研究者争论的一个重要问题,虽然形成很多种说法,但都不是戏剧之源。本文从中国古代戏剧的基本元素出发来探讨戏剧的源流,并提出戏剧起源于人类原初状态时的体态语言的观点。