随机逼近

ABSTRACT This dissertation proposes a number of extended theories of stochastic Petri net and other algorithms to evaluate the performance of various computer networks.

本文提出了一系列随机Petri网的扩展理论和逐次迭代逼近算法，从理论分析角度深入分析了各种计算机网络的多项性能指标。

It is shown that the Chebyshev polynomial approximation is a valid method for the investigation of non-smooth systems.

研究表明，Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法。

Both the numerical results of these two chapters show that the Chebyshev polynomial approximation is an effective method in the study of system with random parameter.

数值结果表明Chebyshev正交多项式逼近法对于分析谐和激励和脉冲激励共同作用下的含有界随机参数系统的分岔现象也是有效的。

Numerical simulations show that similar to their counterpart in deterministic nonlinear system some symmetry-breaking bifurcation may occur in the stochastic Duffing-Van der pol system, and Chebyshev polynomial approximation is an effective approach in solving dynamical problems of nonlinear system with random parameter.

数值模拟显示随机Duffing-Van der pol系统与确定性均值参数系统有着类似的对称破裂分岔行为，文中的主要数值结果表明Chebyshev多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法。

Numerical results for the original stochastic Duffing-van der Pol system obtained separately by the Mento-Carlo method and the Chebyshev polynomial approximation are compared to show the effectiveness and efficiency of the latter method in solving the nonlinear dynamical problems of system with bounded random parameters.

数值模拟结果显示，Chebyshev正交多项式逼近法是研究含有界随机参数的耦合非线性动力学系统的一种有效方法。

In this paper,the authors give a strict proof of geometric Brown motion displayed by stock prices using the methods of approximation from discrete process to continuous stochastic process.

通过由一般的离散过程逼近连续随机过程的方法，给予证券价格按有漂移率的几何布朗运动变化的一个严格的证明，并指出了股票价格过程的一般模型

The experimental results show that this method improves the measurement precision of true temperature and spectral emissivity.

3评估随机噪声对亮温逼近法及连续测量法的影响。

The main procedures are as following: to generate small increment of parameters automatically and to calculate the FE several times and obtain the sensitivity of objective function to the parameters, and then form a Hermite polynomial approximation, the calculation of FE solutions are substitute by the calculation of polynomial approximation, so time cost decreases dramatically.

用n维埃尔米特插值技术建立设计变量在可行域上的目标函数的逼近函数；将局部寻优的梯度算法和全局寻优的随机算法结合起来，大幅度地降低寻优过程中电磁场的计算次数。

Stationary NA sequences; empirical measure; large deviations principle; linear processes; functional law of the iterated logarithm; strong approximations; LPQD sequences; m-dependent random element; precise asymptotics; the central limit theorem for the sum of random number

基础科学，数学，概率论、数理统计平稳NA序列；经验测度；大偏差原理；线性过程；泛函型重对数律；强逼近； LPQD序列； m-相依随机元；精确渐近性；随机指标中心极限定理

Based on the recent situation and trend of the nonlinear systems, we present some recent developments and important problems in stochastic dynamics such as response, bifurcation , chaos, synchronization and control.

摘要介绍了非线性随机动力学的响应、分岔、混沌以及混沌同步与控制的研究现状和发展趋势，探讨了随机复动力系统、时滞系统、逼近方法和数值方法研究中的若干问题及其进展。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。