This work develops an algorithm for global optimization. The algorithm is of gradient ascent type and uses random perturbations. In contrast to the annealing type procedures, the perturbation noise intensity is large. We demonstrate that by properly varying the noise intensity, approximations to the global maximum can be achieved. We also show that the expected time to reach the domain of attraction of the global maximum, which can be approximated by the solution of a boundary value problem, is finite. Discrete-time algorithms are proposed; recursive algorithms with occasional perturbations involving large noise intensity are developed. Numerical examples are provided for illustration.
Based on the weekly closing price of Shenzhen Integrated Index, this article studies the volatility of Shenzhen Stock Market using three different models： Logistic, AR（1） and AR（2）. The time-variable parameters of Logistic regression model is estimated by using both the index smoothing method and the time-variable parameter estimation method. And both the AR（1） model and the AR（2） model of zero-mean series of the weekly dosing price and its zero-mean series of volatility rate are established based on the analysis results of zero-mean series of the weekly closing price, Six common statistical methods for error prediction are used to test the predicting results. These methods are： mean error （ME）, mean absolute error （MAE）, root mean squared error （RMSE）, mean absolute percentage error （MAPE）, Akaike＇s information criterion （AIC）, and Bayesian information criterion （BIC）. The investigation shows that AR（1） model exhibits the best predicting result, whereas AR（2） model exhibits predicting results that is intermediate between AR（1） model and the Logistic regression model.
This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument. In addition, easily verifiable conditions on drift and diffusion coefficients are also given. Moreover, examples are supplied for demonstration purposes.
Power control problems for wireless communication networks are investigated in direct-sequence codedivision multiple-access （DS/CDMA） channels. It is shown that the underlying problem can be formulated as a constrained optimization problem in a stochastic framework. For effective solutions to this optimization problem in real time, recursive algorithms of stochastic approximation type are developed that can solve the problem with unknown system components. Under broad conditions, convergence of the algorithms is established by using weak convergence methods.
通过运行SPSS,建立L og istic回归信用评价模型(cred it eva luation m odel),用来对中国2000年106家上市公司进行两类模式分类,这两类模式是指按照公司的经营状况分为“差”和“正常”两个小组.对每一家上市公司,考虑其经营状况的4个主要财务指标:每股收益、每股净资产、净资产收益率和每股现金流量.仿真结果表明,L og istic回归信用评价模型对总体106个样本,判别准确率达到99.06%.此外,本文的研究结果还发现,当利用SPSS的D iscrim inan t给出的模型系数建立的线性判别分析模型和利用SPSS的M u ltinom ia lL og istic给出的模型参数建立的L og istic回归模型,L og istic回归模型的判别结果不如线性判别模型.但如果剔除不合格的样本,或是将样本数据规格化,则可以提高L og istic回归模型的分类准确率.
