非寿险分类费率模型及其参数估计

在非寿险分类费率厘定中,存在各种模型可供选择,如加法模型、乘法模型、混合模型和广义线性模型等,而在这些模型的参数估计中,还存在各种可供选择的估计方法,如最小二乘法、极大似然法、最小x2法、直接法和边际总和法等。这些模型和参数估计方法散见于各种精算学文献中,本文对这些模型和参数估计方法进行了系统的比较和分析,并揭示了它们之间存在的一些等价关系。     

The Heat Equation with Initial Data Corrupted by Measurement Error and Missing Data

In this work the Cauchy problem for the one-dimensional heat equation is considered. In contrast to existing literature it is assumed that the initial state f is unknown and that information regarding f is obtained by some process of measurement. To enhance realism, both measurement errors and missing data are allowed for. Under assumptions on f in the Fourier-domain first an approximation to f is derived from the data by means of a novel uncertainty principle. Then, it is studied how this perturbation in the initial state propagates with time.      

Randomized UMD Banach spaces and decoupling inequalities for stochastic integrals

In this paper we prove the equivalence of decoupling inequalities for stochastic integrals and one-sided randomized versions of the UMD property of a Banach space as introduced by Garling.

     

非线性Kundu方程的弱守恒差分格式

本文考察了一类非线性Kundu方程的周期初值问题,提出了一种弱守恒的差分格式,对其差分解作了先验估计,证明了格式的收敛性与稳定性,最后,通过数值计算检验了格式的可信性.     

Pattern Search Method for Discrete <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging. This work was supported by M.U.R.S.T., Rome, Italy.     

Bivariate Blending Thiele-Werner＇s Osculatory Rational Interpolation

Both the expansive Newton＇s interpolating polynomial and the Thiele-Werner＇s interpolation are used to construct a kind of bivariate blending Thiele-Werner＇s osculatory rational interpolation. A recursive algorithm and its characteristic properties are given. An error estimation is obtained and a numerical example is illustrated.     

关于一类具有有界不确定性数据的参数估计方法的误差分析

指出了一类具有有界不确定性数据的参数估计方法存在估计误差这一事实,分析了估计误差存在的原因,给出了估计误差的上界.     

H1弱拓扑中GBBM方程整体吸引子的存在性

文章讨论无界区域上GBBM方程的Cauchy问题,对方程的解进行了先验估计,并证明了在H1弱拓扑中整体吸引子的存在性.     

基于果蝇算法优化广义回归神经网络的矢量水听器的DOA估计

为了提高矢量水听器阵列对窄带信号的DOA估计精度,运用果蝇算法优化广义回归神经网络,通过对阵列协方差矩阵实值化,并提取信号子空间的基作为样本特征进行网络训练,构建了果蝇算法优化下的广义回归神经网络,实现了基于矢量水听器阵列的水下声源的DOA估计.仿真实验结果表明,方法泛化性能较好,能解决输入维数过大的问题,且运行时间短,DOA估计精度高,具有较强的工程应用价值.     

A note on functional a posteriori estimates for elliptic optimal control problems

In this work, new results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed, and fully computable lower bounds for the cost functional in addition to the already existing upper bounds. Using both, the lower and the upper bounds, we arrive at two‐sided estimates for the cost functional. We prove that these bounds finally lead to sharp, guaranteed and fully computable upper estimates for the discretization error in the state and the control of the optimal control problem. First numerical tests are presented confirming the efficiency of the a posteriori estimates derived. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 403–424, 2017