On first passage time structure of random walks

For continuous time birth-death processes on {0,1,2,…}, the first passage time T⁺_n from n to n + 1 is always a mixture of (n + 1) independent exponential random variables. Furthermore, the first passage time T_0,n+1 from 0 to (n + 1) is always a sum of (n + 1) independent exponential random variables. The discrete time analogue, however, does not necessarily hold in spite of structural similarities. In this paper, some necessary and sufficient conditions are established under which T⁺_n and T_0,n+1 for discrete time birth-death chains become a mixture and a sum, respectively, of (n + 1) independent geometric random variables on {1,2,…};. The results are further extended to conditional first passage times.     

左截断相依数据下条件分位数的双核局部线性估计

本文在左截断相依数据下,利用局部线性估计的方法,先提出了条件分布函数的双核估计;然后利用该估计导出了条件分位数的双核局部线性估计,并建立了这些估计的渐近正态性结果;最后,通过模拟显示该估计在偏移和边界点调节上要比一般的核估计更好.     

基于GA-ELM的水上交通事故严重程度影响因素识别研究

水上交通事故严重程度影响因素的识别对从根本上减少严重事故件数、降低事故危害和损失具有重要意义。在历史事故报告的基础上,构建并量化事故影响因素集,提出以极限学习机(ELM)为一般事故、严重事故的二分类器,以遗传算法(GA)为因素搜索算法的GA-ELM因素识别模型。对发生在我国水域的737件水上交通事故进行实证研究,并与以支持向量机(SVM)为分类器的GA-SVM模型进行对比分析。结果表明,GA-ELM模型识别出时段、人为致因、环境致因等9个事故严重程度影响因素,较GA-SVM模型结果更为精简,且分类精度较不做因素识别时分别提高8.2%、7.1%。此外,GA-ELM大大缩短运算时间。由此可见,GA-ELM可为水上交通事故严重程度影响因素识别提供一个较好的方法。     

Iterated conditional expectations

Consider the probability space ([0,1),B,λ), where B is the Borel σ-algebra on [0,1) and λ the Lebesgue measure. Let f=₁[0,1/2) and g=₁[1/2,1). Then for any ε>0 there exists a finite sequence of sub-σ-algebras Gj⊂B(j=1,…,N), such that putting f₀=f and fj=E(fj−1|Gj), j=1,…,N, we have ‖fN−g_‖∞<ε; here E(⋅|Gj) denotes the operator of conditional expectation given σ-algebra Gj. This is a particular case of a surprising result by Cherny and Grigoriev (2007) [1] in which f and g are arbitrary equidistributed bounded random variables on a nonatomic probability space. The proof given in Cherny and Grigoriev (2007) [1] is very complicated. The purpose of this note is to give a straightforward analytic proof of the above mentioned result, motivated by a simple geometric idea, and then show that the general result is implied by its special case.     

Musielak-Orlicz-Sobolev空间关于最大值范数的端点

自20世纪以来,Sobolev空间作为有着重要价值的数学模型而受到广泛关注.它在偏微分方程中有着非常重要的作用.而Musielak-Orlicz-Sobolev空间是将Sobolev空间中的L~p(Ω)空间推广到Musielak-Orlicz空间L_M(Ω)之后形成的空间.因而Musielak-Orlicz-Sobolev空间具有Musielak-Orlicz空间和Sobolev空间中的一些性质.讨论了赋最大值范数的Musielak-Orlicz-Sobolev空间端点的性质.这里的最大值范数指:最大值Luxemburg范数和最大值Amemiya-Orlicz范数.主要得到了Musielak-Orlicz-Sobolev空间关于最大值范数端点的充分条件,并指出这类空间都不是严格凸的.     

不同类型随机变量和差积商的分布

研究两种不同类型的随机变量,即离散型随机变量ζ与连续型随机变量η的和（ζ＋η）、差（ζ-η）、积（ζη）、商（ζ/η）的分布,给出这些分布的密度函数．     

基于POT方法的极值理论在基金净值预测中的应用

为对基金净值数据进行建模,根据基金净值样本数据的尾部特点,建立极大,极小值分布的GPD模型,运用POT方法确定临界值,进而对参数进行估计,并对模型进行检验.最后,运用建立的模型对一些极值点进行预测.所得结果很好地描述了数据特点,对极值点的预测符合实际.     

非线性模型滞后相依的广义互信息检验

The general mutual information （GMI） and general conditional mutual information （GCMI） are considered to measure lag dependences in nonlinear time series. Both of the measures have the property of invariance with transform. The statistics based on GMI and GCMI are estimated using the correlation integral. Under the hypothesis of independent series, the estimators have Gaussian asymptotic distributions. Simulations applied to generated nonlinear series demonstrate that the methods appear to find frequently the correct lags.