一类n阶拟线性奇异摄动边值问题的一致有效渐近展开

本文研究一类ｎ阶拟线性奇异摄动边值问题：εｙ（ｎ）＝ｆ（ｔ，ε，ｙ，…，ｙ（ｎ－２）ｙ（ｎ－１）＋ｇ（ｔ，ε，ｙ，…，ｙ（ｎ－２），ｐｊ（ε）ｙ（ｊ）（０，ε）－ｑｊ（ε）ｙ（ｊ＋１）（０，ε）＝αｊ（ε）（０≤ｊ≤ｎ－２），ｂ１（ε）ｙ（ｎ－２）（１，ε）＋ｂ２（ε）ｙ（ｎ－１）（１，ε）＝β（ε），其中ε＞０为小参数．在较一般的条件之下，应用Ｂａｎａｃｈ／Ｐｉｃａｒｄ不动点定理证明了摄动解的存在性及局部唯一性，并给出了摄动解直到ｎ阶导函数的一致有效渐近展开式，推广和改进了已有的结果［１－５］．     

污染数据回归分析中参数的最小一乘估计

考虑简单回归模型：ｙｉ＝ｘ′ｉβ＋ｅｉ,ｉ＝１,…,ｎ。其中Ｅｅｉ＝０,Ｅｅ＾２ｉ＝σ＾２１。假设ｙ１,ｙ２,…,ｙｎ受到另一独立同分布随机变量序列μ１,μ,…,μｎ的污染,我们仅能观察到污染数据ｙ＾＊ｉ＝（１－ν）ｙｉ,ν为未知的污染参数。本文用污染数据给出了β的最小一乘估计,并证明了它的渐近正态性和相合性。     

具连续变量的线性时滞差分方程的振动性

本文研究如下具有连续变量的线性时滞差分方程ｙ（ｔ）－ｙ（ｔ－τ）＋∑ｍｊ＝１ｐｊ（ｔ）ｙ（ｔ－σｊ）＝０,ｔ≥０,其中ｐｊ（ｔ）∈ｃ（Ｒ＾＋,Ｒ＾＋）,０〈τ〈σ１≤σ２≤…≤ｍ,ｊ＝１,２,…,ｍ,获得了该方程的每个解都振动的若干充分条件,改进了现有文献中的结果。     

一个部份自回归模型的渐近有效性

本文考虑部分自回归模型Ｘｔ＝ｘｔ－１β＋ｇ（Ｕｔ）＋εｔ，ｔ≥１。这里ｇ是一未知函数，β是和待估参数，εｊ是具有０均值和方差σ＾２的ｉ．ｉ．ｄ．误差，Ｕｔｉ．ｉ．ｄ．服从［０，１］上均匀分布。     

变量满足多个线性关系且部分变量带误差的回归分析

考虑独立变量ａ１ｔ，ａｐｔ，它们满足ｍ（≥１）个线性回归关系，ｐΣｊ＝１ｂｉｊａｊｔ＝ｃｉ，ｉ＝１，ｍ，这些变量中的一些，比如ａｉｔ（ｉ＝ｒ＋１，ｐ）可以被确切观测到，而另一些变量的观测值带有误差。即ａｉｔ的观测值为ｘｉｔ＝ａｉｔ＋∈ｉｔ（ｉ＝１，ｒ，ｔ＝１，ｎ），而ｘｉｔ＝ａｉｔ（ｉ＝ｒ＋１，ｐ，ｔ＋１，ｎ），在?ｔ＝（∈１ｔ，∈ｒｔ）ｔ，ｔ＝１，ｎ为ｉｉｄ。且Ｅ∈ｔ＝０，Ｅ∈ｔ∈ｔｒ＝σ＾２Ｉ     

污染数据半参数回归模型估计的渐近正态性

考虑半参数回归模型：ｙｉ＝ ｘｉβ＋ ｇ（ｔｉ）＋ ｅｉ,ｉ＝ １,２,…,ｎ．其中 Ｅｅｉ＝ ０, Ｅｅ２ｉ＝ σ２１ ＞ ０．假定ｙ１,ｙ２,…,ｙｎ 受到另一独立同分布随机变量序列 μ１,μ２,…,μｎ 的污染,｛μｉ｝与｛ｙｉ｝独立,且仅能观察到污染数据．文［１］对由污染数据作出的参数 β的估计 βｎ,证明了它的强相合性,而本文则证明了它的渐近正态性     

n维时滞Prajneshu生态系统的区间生态稳定

对ｎ维时滞Ｐｒａｊｎｅｓｈｕ＾［１］生态系统ｄｘｉ（ｔ）／ｄｔ＝ｘｉ（ｔ）［ｒｉ＋Σ↑ｎ↓ｊ＝１ａｉｊｌｎｘｊ＋Σ↑ｎ↓ｊ＝１ｂｉｊｌｎｘｊ（ｔ－τｊ）ｉ＝１，２，…，ｎ（１）的区间生态稳定性进行了研究，给出了其区间生态稳定的判别准则。     

相依回归系统一种协方差改进估计之协方差阵的无偏估计

考虑相依回归方程系统ｙｉ＝Ｘｉβｉ＋εｉ（ｉ＝１，２），Ｅ（εｉ）＝０，Ｃｏｖ（εｉ，εｊ）＝σｉｊＩｎ。记βｉ为βｉ的协方差改进估计＾［１］。σｉｊ未知时，记βｉ为用非限定估计σｉｊ代替βｉ中的σｉｊ得到的两步估计，并记βｉ为用限定估计σｉｊ代替βｉ中的σｉｊ得到的两步估计，这两种两步估计的协方差中含有未知参数σｉｊ代替βｉ中的σｉｊ得到的两步估计，这两种两步估计的协方差中含有未知参数σｉｊ。本     

The Structure and Stabilization Decom position of Linear Interconnected ControlSystem swith Multidelays

§１．　ＴｈｅＥｑｕｉｖａｌｅｎｃｅｏｆＬｙａｐｕｎｏｖｓＲａｎｇｅｏｆｔｈｅＩｎｔｅｒｃｏｎｎｅｃｔｅｄＳｔａｂｉｌｉｚａｔｉｏｎＮｅｗ，ｌｅｔｕｓｃｏｎｓｉｄｅｒｔｈｅｌｉｎｅａｒｃｏｎｓｔａｎｔｉｎｔｅｒｃｏｎｎｅｃｔｅｄｃｏｎｔｒｏｌｓｙｓｔｅｍｘｉ（ｔ）＝∑ｎｊ＝１ａｉｊｘｊ（ｔ）＋∑ｍｊ＝１ｂｉｊｕｊ（ｔ）＋∑Ｎ１ｒ＝１∑ｎｊ＝１ａ（ｒ）１ｉｊｅ（ｒ）１ｉｊｘｊ（ｔ）　　　　　　　　　　＋∑Ｎ２ｓ＝１∑ｎｊ＝１ａ（ｓ）２ｉｊｅ（ｓ）２ｉｊｘｊ（ｔ－ｒ（ｓ）１ｉｊ）＋∑Ｎ２ｄ＝１∑…     

脉冲中立型时滞微分方程解的振动性

本文讨论一阶脉冲中立型时滞微分方程［ｙ（ｔ）＋Ｐｙ（ｔ－σ）］′＋Ｑ（ｔ）ｙ（ｔ－σ）＝０，ｔ０，ｔ≠ｔｋ，ｋ＝１，２，…，ｙ（ｔ＋ｋ）－ｙ（ｔ－ｋ）＝ｂｋｙ（ｔｋ），ｋ＝１，２，…，｛（Ｅ）这里τ，σ，Ｐ均为常数，τ＞０，σ＞０，Ｑ（ｔ）∈Ｃ（［０，∞），Ｒ＋），ｂｋ＞－１，ｋ＝１，２，…．分三种情况，Ｐ－１；－１＜Ｐ＜０；Ｐ＞０给出了方程（Ｅ）所有解振动的充分条件．     

Some consequences of estimating parameters for the M/M/1 queue

An important interface between stochastic models and actual systems comes in estimating values for model parameters using “real world” data. This interface between models and systems is studied for one of the most elementary stochastic systems, the M/M/1 queue. Estimating arrival rates and service rates results in a notable discrepancy between the state distribution for the model (estimated parameters) and the state distribution for the actual system (known parameters). Also, the expected number of customers in the model is infinite regardless of the (unknown) value of the actual traffic intensity. The truth of this assertion is obvious if one allows estimated traffic intensities to equal or exceed one. However, it is shown that the mean for the model is infinite even if the estimated traffic intensity is restricted to be strictly less than one.     

A parameter estimation scheme for a class of sequential hybrid systems

It may happen that the equations governing the response of dynamical systems have some parameters whose values may not be known a priori and have to be obtained using parameter estimation schemes. In this article, we present a parameter estimation scheme for a class of sequential hybrid systems. By hybrid systems, we refer to those systems whose response is described by different governing equations corresponding to various regimes/modes of operation along with some criteria to switch between the same. In a sequential hybrid system, the different modes are arranged in a specific sequence and the system can switch from a given mode to either the previous mode or the following mode in this sequence. Here, we consider those systems whose governing equations consist of ordinary differential equations and algebraic equations. The conditions for switching between the various modes (referred to as transition conditions) are in the form of linear inequalities involving the system output. We shall first consider the case where the transition conditions are known completely. We present a parameter update scheme along with sufficient conditions that will guarantee bounded parameter estimation errors. Then, we shall consider the case where the transition conditions are not known in the sense that some parameters in these conditions are not known. We present a parameter estimation scheme for this case. We illustrate the performance of the parameter estimation scheme in both cases with some examples.     

Guaranteed nonlinear parameter estimation in knowledge-based models

Knowledge-based models are ubiquitous in pure and applied sciences. They often involve unknown parameters to be estimated from experimental data. This is usually much more difficult than for black-box models, only intended to mimic a given input–output behavior. The output of knowledge-based models is almost always nonlinear in their parameters, so that linear least squares cannot be used, and analytical solutions for the model equations are seldom available. Moreover, since the parameters have some physical meaning, it is not enough to find some numerical values of these quantities that are such that the model fits the data reasonably well. One would like, for instance, to make sure that the parameters to be estimated are identifiable. If this is not the case, all equivalent solutions should be provided. The uncertainty in the parameters resulting from the measurement noise and approximate nature of the model should also be characterized. This paper describes how guaranteed methods based on interval analysis may contribute to these tasks. Examples in linear and nonlinear compartmental modeling, widely used in biology, are provided.     

关于图的若干介值问题

对连通图G,以C_i(G),■(G)分别表G的有i条边的连通支撑子图之集与连通子图之集,以C~i(G),(?)(G)分别表G的顶点数为i的子树集与连通子图之集.本文讨论了这四类子图簇对若干基本参数及端点数的介值性,从而对已有的一些结果作了若干有意义的拓广.     

也谈洛特卡分布的参数估计

本文分析了论文〔１〕参数估计的结果与过程，并给出估计洛特卡分布参数的一种方法．     

外表设计及其案例研究（Ⅲ）

本篇给出了在外表设计方法的比较中关于八个案例［２］的一些数据结果。并对在外表设计的比较过程中所发现的一些问题进行了探讨。     

Robust nonuniform dichotomies and parameter dependence

We establish the robustness of linear cocycles with an exponential dichotomy, under sufficiently small Lipschitz perturbations, in the sense that the existence of an exponential dichotomy for a given cocycle persists under these perturbations. We consider cocycles in Banach spaces, as well as the general case of nonuniform exponential dichotomies, and also the general case of an exponential behavior ecρ(n), given by an arbitrary sequence ρ(n) including the usual exponential behavior ρ(n)=n as a very special case. Moreover, we show that the projections of the exponential dichotomies obtained from the perturbation vary continuously with the parameter, and in fact that they are locally Lipschitz on finite-dimensional parameters.     

Stochastic Approximation Algorithms for Parameter Estimation in Option Pricing with Regime Switching

Abstract

This work is concerned with option pricing. Stochastic approximation/optimization algorithms are proposed and analyzed. The underlying stock price evolves according to two geometric Brownian motions coupled by a continuous-time finite state Markov chain. Recursive stochastic approximation algorithms are developed to estimate the implied volatility. Convergence of the algorithm is proved. Rate of convergence is also ascertained. Then real market data are used to compare our algorithms with other schemes.     

Model-Based Recursive Partitioning

Recursive partitioning is embedded into the general and well-established class of parametric models that can be fitted using M-type estimators (including maximum likelihood). An algorithm for model-based recursive partitioning is suggested for which the basic steps are: (1) fit a parametric model to a dataset; (2) test for parameter instability over a set of partitioning variables; (3) if there is some overall parameter instability, split the model with respect to the variable associated with the highest instability; (4) repeat the procedure in each of the daughter nodes. The algorithm yields a partitioned (or segmented) parametric model that can be effectively visualized and that subject-matter scientists are used to analyzing and interpreting.     

Logistic模型参数估计及预测实例

本文提出了对Ｌｏｇｉｓｔｉｃ模型中的参数进行迭代估计的新算法，通过比较分析，说明了本文算法的有效性。