New types of 3-D systems of quadratic differential equations with chaotic dynamics based on Ricker discrete population model

The wide class of 3-D autonomous systems of quadratic differential equations, in each of which either there is a couple of coexisting limit cycles or there is a couple of coexisting chaotic attractors, is found. In the second case the couple consists of either Lorentz-type attractor and another attractor of a new type or two Lorentz-type attractors. It is shown that the chaotic behavior of any system of the indicated class can be described by the Ricker discrete population model: z_i+1 = z_i exp(r − z_i), r > 0, z_i > 0, i = 0, 1, … . The values of parameters, at which in the 3-D system appears either the couple of limit cycles or the couple of chaotic attractors, or only one limit cycle, or only one sphere-shaped chaotic attractor, are indicated. Examples are given.     

On the expected discounted penalty function for risk process with tax

In this paper we consider the generalized Cramér-Lundberg risk model including tax payments. We investigate how tax payments affect the behavior of a Cramér-Lundberg surplus process by defining an expected discounted penalty function at ruin. We derive an explicit expression for this function by solving a differential equation. Consequently, the explicit formulas for the discounted probability density function of the surplus immediately before ruin and the discounted joint probability density function of the surplus immediately before ruin and the deficit at ruin are obtained. We also give explicit expressions for the function for exponential claims.     

外加电场对光折变高阶响应影响的微扰分析

应用微扰展开法了“跳跃模型”给出了空间电荷场前三阶分量随时间，外加电场等变化的解析表达式，同时讨论了外加电场对各阶空间电荷场建立的影响，当扩散与外加电场可比拟时，外加电场对空间电荷场的影响不大，随着空间电荷场阶数的提高，其达到最大饱和值所需的外加电磁越小，在外加电场作用下，空间电荷场各阶分量随时间呈振荡衰减，直到达到饱和，外加是场越大，振荡越强烈，周期越短，在考虑高阶分量的贡献后，空间电荷场的振荡     

辐射驱动内爆温度源脉冲整形研究

辐射驱动温度源脉冲整形是获得高压缩比的重要途径。本文从脉冲整形的基本原理出发，采用数值模拟方法，给出适合于神光Ⅲ装置内爆实验的辐射驱动温度源脉冲整形曲线。     

Falling and explosive,dormant, and rising markets via multiple‐regime financial time series models

A multiple‐regime threshold nonlinear financial time series model, with a fat‐tailed error distribution, is discussed and Bayesian estimation and inference are considered. Furthermore, approximate Bayesian posterior model comparison among competing models with different numbers of regimes is considered which is effectively a test for the number of required regimes. An adaptive Markov chain Monte Carlo (MCMC) sampling scheme is designed, while importance sampling is employed to estimate Bayesian residuals for model diagnostic testing. Our modeling framework provides a parsimonious representation of well‐known stylized features of financial time series and facilitates statistical inference in the presence of high or explosive persistence and dynamic conditional volatility. We focus on the three‐regime case where the main feature of the model is to capturing of mean and volatility asymmetries in financial markets, while allowing an explosive volatility regime. A simulation study highlights the properties of our MCMC estimators and the accuracy and favourable performance as a model selection tool, compared with a deviance criterion, of the posterior model probability approximation method. An empirical study of eight international oil and gas markets provides strong support for the three‐regime model over its competitors, in most markets, in terms of model posterior probability and in showing three distinct regime behaviours: falling/explosive, dormant and rising markets. Copyright © 2009 John Wiley & Sons, Ltd.     

Exchangeable claim sizes in a compound Poisson‐type process

When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson‐type processes. In particular, exchangeability is achieved through conditional independence, using parametric and nonparametric measures for the conditioning distribution. Bayes' theorem is employed to ensure an arbitrary but fixed marginal distribution for the claim sizes. A full Bayesian analysis of the proposed model is illustrated with a panel‐type data set coming from a Medical Expenditure Panel Survey (MEPS). Copyright © 2009 John Wiley & Sons, Ltd.     

基于ARIMA与神经网络集成的GDP时间序列预测研究

本文深入分析了单整自回归移动平均(ARIMA)模型与神经网络(NN)模型的预测特性和优劣,并在此基础上建立了由ARIMA模型和NN模型集成的GDP时间序列预测模型与算法。其基本思想是充分发挥两种模型在线性空间和非线性空间的预测优势,据此将GDP时间序列的数据结构分解为线性自相关主体和非线性残差两部分,首先用ARIMA模型预测序列的线性主体,然后用NN模型对其非线性残差进行估计,最终集成为整个序列的预测结果。仿真实验表明:集成模型的预测准确率显著高于单一模型的预测准确率,从而证实了集成模型用于GDP预测的有效性。     

求解线性模型稳健参数估计的整数编码遗传算法

线性模型回归系数的一些稳健估计如LMS、LQS、LTS、LTA的应用越来越广泛,然而它们的精确计算依赖于NP难题,在遇到高维大规模数据集时不可能在较短时间内得到精确解.为尽快得到较高精度的近似解,提出了求解线性模型的稳健参数估计的整数编码遗传算法,通过计算机模拟试验验证了算法可以更快地找出全局最优解.     

基于线性状态反馈的非线性混合系统的实用稳定化

研究非线性混合系统的实用稳定化问题,其中该系统具有时变子系统和时变跳转函数.首先,通过状态跳转函数,确定系统一条严格递增的切换时间序列.然后在该序列中的每一段时间区间内,明确地构造出相应的线性状态反馈控制律,由此实现闭环系统的实用稳定.最后,给出一个数值例子说明文中方法的有效性.     

基于时间序列模型的全国30家电台收视率分析

以湖南电视台和北京卫视为代表,对全国30家电视台卫星频道2008全年日收视率进行时间序列分析,建立了四种拟合模型.其中,大部分电台收视率具有长期趋势或长期趋势和季节效应的综合影响,分别建立ARIMA模型和乘积季节模型,并进行预测,其结果表明模型拟合效果较好.