The dependence of extreme values of discrete and continuous time strongly dependent Gaussian processes

In this note, the asymptotic relation between the maximum of a continuous strongly dependent stationary Gaussian process and the maximum of this process sampled at discrete time points is studied. It is shown that these two extreme values are asymptotically totally dependent no matter what the grid of the discrete time points is.     

The oscillation of the occupation time process of super- Brownian motion on Sierpinski gasket

The occupation time process of super-Brownian motion on the Sierpinski gasket is studied. It is shown that this process does not possess stable property in the long run, but oscillates periodically in some sense. Other convergence properties are also studied.     

基于动态参照点的损失厌恶投资组合优化模型

在连续时间下,考虑损失厌恶投资者参照点的动态调整特征,构建基于动态参照点的损失厌恶投资组合模型,使用鞅方法对模型进行求解,得到最优风险资产权重的解析表达式。并计算损失厌恶投资者在参照点动态调整条件下的预期最优期末财富。进一步应用数值算例,分析投资者的参照点动态调整幅度和损失厌恶水平对模型最优风险资产权重和预期最优期末财富的影响。     

Compatibility of multi-wave panel data and the continuous-time homogeneous Markov chain. An analysis of a continuous-time process by means of discrete-time longitudinal observations

Multi-wave panel data are observations at two or more points in time on a continuously changing attribute of interest (e.g. behaviour). In this paper, the adequacy of the continuous-time homogeneous Markov chain (CTHMC) model is assessed for describing the process of change underlying such data. In the case of equidistant observational times, it may happen that the maximum-likelihood estimate of the transition probability matrix between successive observational times from these data cannot arise from a CTHMC. It is investigated whether this event can be ascribed to chance through the introduction of an hypothesis test. © 1998 John Wiley & Sons, Ltd.     

Dependence Between Extreme Values of Discrete and Continuous Time Locally Stationary Gaussian Processes

The maximum of a continuous, locally stationary Gaussian process which satisfies Bermans condition on the long range dependence is compared with the maximum of this process sampled at discrete time points. These two extreme values are asymptotically totally dependent if the grid of the discrete time points is sufficiently dense, and asymptotically independent if the the grid points are sparse.AMS 2000 Subject Classification. Primary—60F05, Secondary—60G15     

BOUNDARY VALUE PROBLEM TO DYNAMIC EQUATION ON TIME SCALE

In this paper we consider a nonlinear first-order boundary value problem on a time scale. The existence results of three positive solutions are obtained using fixed point theorems. Finally,examples are presented to illustrate the main results.     

生灭过程的Ito游程理论

当生灭过程不唯一,且附加的虚状态∞是"瞬时"且正则时,其轨道结构是异常复杂的.主要工作是利用Ito的游程理论来分析处理这种生灭过程,研究其轨道性质,并最终得到预解式.此预解式具有清楚的概率意义,能够直观地反映生灭过程的轨道结构.     

基于时间序列的挖掘算法在流程工业产品质量控制模型中的应用

针对目前流程工业产品质量控制采用人工检查和统计质量控制方法,缺乏产品质量预先预报以及时时调整生产过程的工艺参数存在一定困难.利用生产过程采集到的实际数据,采用基于时间序列的动态数据挖掘技术和BP神经元网络,预测产品质量和分析产品生产过程的工艺,最大限度减少不合格产品的产出,提高生产效率.根据上述理论建立流程工业数据动态质量控制平台,以中厚钢板生产过程为例,应用表明了这种方法在实际应用中的正确性和有效性.     

Saddle points for maximin investment problems with observable but non-predictable parameters: solution via heat equation{dagger}

^** Email: nikolai.dokuchaev{at}ul.ie We study optimal investment problem for a market model wherethe evolution of risky assets prices is described by Itô'sequations. The risk-free rate, the appreciation rates and thevolatility of the stocks are all random; they depend on a randomparameter that is not adapted to the driving Brownian motion.The distribution of this parameter is unknown. The optimal investmentproblem is stated in a ‘maximin’ setting to ensurethat a strategy is found such that the minimum of expected utilityover all possible distributions of parameters is maximal. Weshow that a saddle point exists and can be found via a solutionof the standard 1D heat equation with a Cauchy condition definedvia one dimensional minimization. This solution even coversmodels with unknown solution for a given distribution of themarket parameters.     

多类顾客多服务台队列网络的高负荷极限定理

多类顾客多服务台队列网络广泛地应用到计算机网络、通讯网络和交通网络 .由于系统的复杂性 ,其数量指标的精确解很难求出 .为了寻求逼近解 ,本文用概率测度弱收敛理论对进行了研究 ,在高负荷的条件下 ,我们获得了网输入过程、闲时过程和负荷过程的极限定理 .     

Gk保形分段2k次参数多项式插值

An interpolation scheme constructing shape preserving piecewise de-gree 2k parametric polynomial curves is presented. For the given data set {Qi＝(x1,yi) }n i-0, the shape preserving interpolation curve is Gk continuous.     

On some inequalities of local time

In this paper, we extend the Barlow-Yor's inequality of local time to the case stopped at a random time.     

First crossing time,overshoot and Appell–Hessenberg type functions

We consider a general insurance risk model with extended flexibility under which claims arrive according to a point process with independent increments, their amounts may have any joint distribution and the premium income is accumulated following any non-decreasing, possibly discontinuous, real valued function. Point processes with independent increments are in general non-stationary, allowing for an arbitrary (possibly discontinuous) claim arrival cumulative intensity function which is appealing for insurance applications. Under these general assumptions, we derive a closed form expression for the joint distribution of the time to ruin and the deficit at ruin, which is remarkable, since as we show, it involves a new interesting class of what we call Appell–Hessenberg type functions. The latter are shown to coincide with the classical Appell polynomials in the Poisson case and to yield a new class of the so called Appell–Hessenberg factorial polynomials in the case of negative binomial claim arrivals. Corollaries of our main result generalize previous ruin formulas e.g. those obtained for the case of stationary Poisson claim arrivals.     

一类Fork-Join排队网络的强逼近

本文借助于强逼近理论,对一类Fork-Join排队网络进行了较为细致的研究,得到了在各种负荷条件下响应时间的强逼近定理.     

模糊神经网络中最大最小算子的连续化

1 前言神经网络以其很强的学习能力而著称(文献[1]),但其缺点是不容易纳入人的推理知识,模糊推理系统的优缺点正好与其相反．因此将模糊逻辑与神经网络相结合,形成模糊神经网络(文献[2],[3]),正可以取长补短,集学习,联想,识别,自适应及模糊信息处理于一体．     

The Likelihood of the Parameters of a Continuous Time Vector Autoregressive Model

This paper provides a method of constructing the likelihood function of the parameters of a continuous time vector autoregressive model on the basis of discrete data without requiring the restrictions extant methods impose on the data that are capable of being rejected by a statistical test. In particular, the method does not rely on a steady-state assumption that can rule out unit root processes; it allows for weak assumptions on the innovations; and it allows for a mixture of skip-sampled and temporally-aggregated data. This revised version was published online in August 2006 with corrections to the Cover Date.     

DETERMINATION OF PERMANENT OPTIMAL DATA POINTS AND AN EFFICIENT ALGORITHM FOR LAD PROBLEM

This paper gives a definition of permanent optimal data point of Least Absolute Deviation(LAD)problem.Some theoretical results on non-degenerate LAD problem are obtained.For computing LAD problem,an efficient,algorithm is given according to the idea of permanent optimal data point.Numerical experience shows that our algorithm is better than many of others,including the famous B R algorithm.     

Probabilistic Modelling of Monitoring and Maintenance of Multistate Monotone Systems with Dependent Components

In Gåsemyr and Natvig (2001) partial monitoring of components with applications to preventive system maintenance was considered for a binary monotone system of binary components. The purpose of the present paper is to extend this to a multistate monotone system of multistate components, where the states more realistically represent successive levels of performance ranging from the perfect functioning level down to the complete failure level. We start out close to the spirit of Arjas (1989) by using a marked point process with complete monitoring of all components, and hence of the system, as the basic reference framework. We then consider a marked point process linked to partial monitoring of some components, for instance in certain time intervals. Incorporation of information from the observed system history process is then treated. Mainly, we assume that the inspection strategy is determined by the observed component history process only, with a possible exception of a full or partial autopsy after an observed change of state of , the system. Furthermore, we consider how to arrive at the posterior distribution for the relevant parameter vector by a standard simulation procedure, the data augmentation method. The idea is to extend the observed data to the complete component history process. The theory is applied to an electrical power generation system for two nearby oilrigs with some standby components, as considered in Natvig et al. (1986).AMS 2000 Subject Classification: Primary 96B25; Secondary, 62N05, 60K10     

连续并既约元及其在刻画Fuzzy关系方程解集中的应用

本文首先引入连续并既约元(是并既约元但不是完全并既约元的元)的概念,并讨论了它的性质,然后应用连续并既约元的性质去刻画完备Brouwer格上无限Fuzzy关系方程A☉X=b的解集(其中A=(aj)j∈J和b已知,b为连续并既约元,X= (xj)j∈JT未知,“☉”表示“sup-inf”,J为无限集):给出了方程存在可达解与不可达解的充要条件及可达解与不可达解的一些性质,进一步刻画了方程的解集．