基于随机微分方程的股权拍卖报价策略及模型研究

拍卖是实现风险投资股权退出的方式之一.在风险投资股权拍卖交易中存在的信息不对称以及外部环境的不确定性使得外部投资者难以对风险企业股权准确地定价, 鉴于此,将股权竞买系统视为一个开放系统,运用随机微分方程来描述外部投资者的报价策略状态演变过程,在此基础之上构建风险投资退出股权拍卖模型,并探讨市场出清价格的形成机理及其信息公布程度、竞买人易受影响程度等因素的影响,最后运用变分法对风险投资家的期望收益进行了分析.     

短期降雨预测的随机微分模型

在Nakita等的确定型短期降雨预测模型的基础上，利用随机微分方程理论。给出了预测降雨强度的随机模型．通过随机分析理论，求出了随机模型的解，同时研究了求解的近似数值方法和利用Fourier变换转化该随机降雨模型方程为常微分方程组的可行性．最后把文章提出的随机波动模型和NAk．klta提出的确定型短期预测模型运用到Nakita 1996年给出的降雨事件中进行预测和比较，效果良好．     

Razumikhin-type theorems for asymptotic stability of impulsive stochastic functional differential systems

<正>In this paper,we investigate the pth moment uniformly asymptotic stability of impulsive stochastic functional differential systems by extending some Razumikhin-type theorems.Based on the Lyapunov functions and Razumikhin techniques,some criteria are established and their applications to impulsive stochastic delay systems are proposed.An illustrative example shows the effectiveness of our results.     

求解延迟微分方程的ROSENBROCK方法的渐近稳定性

数值求解延迟微分方程的Rumge-kutta方法和θ－方法已经有了较深入的研究。本文适当改造求解微分方程的Rosenbrock方法，构造了一类求解延迟微分方程的Rosenbrock方法，证明了这类方法是GP－稳定的，而且这类方法的GP－稳定性与求解常微分方程的Rosenbrock方法的A－稳定性等价，数值试验表明这类方法是有效的。     

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

1.INTRODUCTION Considerthefollowingdelaydifferentialequations(DDEs)y′(x)=f(x,y(x),y(x-τ(x))),a≤x≤b y(x)=φ(x),xmin≤x≤a(1)wherey,f,φaren vectorfunctions,φ(x)isinitial valuefunction,τ(x)≥0isdelayfunction.Definition1DDEs(1)issingularatthepoint xαifthelagsatisfiesτ(xα)=0.Ifthereisnosuch pointxα∈[a,b],thentheDDEs(1)isnon singular.InthenumericalsolutionofDDEs(1)byacon tinuousexplicitRunge Kuttamethod,wesuppose thatwehaveanapproximationyntoy(x)atxnand wishtocomputeanapproxima…     

数值求解多延迟中立型系统的渐近稳定性

给出并证明了多延迟中立型系统渐近稳定的克分条件；分析了用线性多步法求解多延迟中立型系统数值解的稳定性，基于Lagrange插值，证明了数值求解多延迟中立型系境的线性多步法渐近稳定的充分必要条件是它是A-稳定的．     

New tracking-differentiator design and analysis of its stability and convergence

A new simple linear tracking-differentiator (T-D) is presented. Stability and convergence of the T-D are thoroughly proved, which avoids inconvenience of stability proof for nonlinear T-D with switch function. Through error analysis, the presented T-D can extract differential of any piecewise smooth nonlinear signals to reach a high accuracy. Compared with the nonlinear T-D with switch function, shaking phenomenon is avoided at the switching point of the function. By further modifying the linear T-D, it can effectively restrain differential impulses produced by initial errors of signals or by signals suddenly changing. Finally, analysis of several simulation examples shows the effectiveness of the proposed theory.     

非线性随机延迟微分方程Euler-Maruyama方法的收敛性

首先利用附近已有节点上的值通过插值对延迟项进行数值逼近,这是一种崭新的尝试;然后针对较一般情形下的一类非线性随机延迟微分方程初值问题,得到了带线性插值的Euler-Maruyama方法在均方意义下是收敛的理论结果,它部分推广了已有文献中的相关结论。     

Stability of stochastic switched epidemic systems with discrete or distributed time delay

Stochastic switched epidemic systems with a discrete or distributed time delay are constructed and investigated. By the Lyapunov method and lto＇s differential rule, the existence and uniqueness of global positive solution of each system is proved. And stability conditions of the disease-free equilibrium of the systems are obtained. Numerical simulations are presented to illustrate the results.     

PERIODIC SOLUTIONS AND GLOBAL ASYMPTOTIC STABILITY OF A DELAYED DISCRETE PREDATOR-PREY SYSTEM WITH HOLLING II TYPE FUNCTIONAL RESPONSE

In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Hoffing Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.     

Convergence and stability of the Newton-Like algorithm with estimation error in optimization flow control

The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed.The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed.Based on the optimization theory,a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained.Furthermore,even when this sufficient condition doesn't hold,this algorithm can also converge,provided a modified step size,and an attraction region is obtained.Based on Lasalle's invariance principle applied to a suitable Lyapunov function,the dynamic system described by this algorithm is proved to be global stability if the error is zero.And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence.All trajectories ultimately converge to the equilibrium point.     

Global exponential stability for delayed cellular neural networks and estimate of exponential convergence rate

Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.