随机扰动下的库存投资决策模型

本文讨论的是库存投资的最优决策问题.不同于确定性q理论,对于引入了市场不确定性扰动的库存控制系统,文章建立了库存投资随机优化决策模型.从市场利率波动的角度对库存决策模型进行分析,得出的结论是:小的市场利率的扰动能够提高企业折现利润的预期,进而导致公司库存投资的上升.     

广义随机Solow经济增长模型

本文在文[1]的基础上进一步拓广了随机Solow经济增长模型．利用白噪声分析理论建立的广义随机Solow经济增长模型，将随机Solow模型推广到包含广义白噪声泛函及具有非可料扩散系数的情形，并且借助U—泛函方法表明了Picard迭代法在此仍十分有效．     

随机Solow模型的平稳分布（英文）

本文重新考虑连续时间随机Solow模型,在Merton(1975)模型的条件下,若噪声相对较小时,资本及利率的随机微分方程存在唯一全局正解.本文证明这两类模型存在唯一的稳定分布.     

一类随机埃博拉传染病模型的动力学行为分析

研究了一类具有疫苗接种和染病者死亡后病毒继续传播的随机埃博拉传染病模型的动力学行为.通过利用It?公式和构造Lyapunov函数等方法,首先证明了随机系统全局正解的存在唯一性;接着分析了随机系统的正解围绕确定性系统的无病平衡点和地方病平衡点的渐近行为;最后通过数值模拟验证了理论结果.所得结果表明环境白噪声对传染病模型平衡点的稳定性有影响.     

连续随机Solow模型的渐近性质

本文重新考虑了随机Solow模型,在Merton(1975)模型的条件下, 证明出描述模型的随机微分方程的解为正值,这补充了Merton的结果.利用随机微分方程平凡解的指数不稳定性并结合Merton的结果,得出资本与劳动的比率或者呈现稳定(渐近)分布, 或者呈指数增长.在这些结果中, 劳动力供给与资本积累的波动起着重要作用.     

带Poisson跳非线性随机种群动力学模型的最优收获控制

研究了一类带跳的非线性随机群体动力学模型的最优收获控制.给出了在外界环境对系统产生影响的条件下带有Poisson跳的随机种群动力学系统;通过随机极大值原理,Hamilton函数及Ito公式,讨论了最优收获控制所满足的充分必要条件,所得到的结论是确定性种群系统的扩展.     

基于变动人口的Solow模型

本文在Solow模型框架中引入随时间变动人口增长函数，并假定人口增长率最终趋于零，证明该模型的解是渐近稳定的，收敛于零人口增长率的经典Solow模型的解。通过引入变动人口增长率，讨论人口过渡时期和人口波动对经济增长的影响，并给出数值计算结果。     

随机Solow经济增长模型及其解的性质

１９８７年诺贝尔（Ｎｏｂｅｌ）经济学奖获得者Ｓｏｌｏｗ教授，建立了确定性的经济增长模型（１９５６年）．它比较真实地描述了现实世界申的确定性的经济增长状况，然而对不确定性的现象，往往误差较大，甚至失效．本文把Ｓｏｌｏｗ模型扩展到随机情形，扩展了Ｂａｎａｃｈ压缩映像原理和不动点定理，获得了随机Ｓｏｌｏｗ模型主要方程和随机解的一些性质．     

Stochastic Modeling and Convergence Analysis of Internet Routers北大核心CSCD

目前建立的路由收敛模型大部分都是确定性模型,而路由器在收敛过程中存在丢包、链路噪声、互连拓扑结构突变等现象。针对这些随机问题,该文引入Bernoulli白序列分布、Wiener过程、Markov过程,提出了一种新的随机动力系统模型,应用随机微分方程理论和随机分析方法得出其路由收敛的充分条件,结果证明,随机环境下路由状态收敛与路由器连接拓扑的Laplace矩阵、Markov切换的平稳分布、网络中数据包的成功传输率以及噪声强度息息相关。最后通过一个数值实例验证了相关结论的有效性。     

具有公共健康教育的随机潜蚤病模型动力学行为研究

潜蚤病是加勒比、拉丁美洲和撒哈拉以南的非洲等经济条件较差地区的一种常见的人畜共患病,其因发病率高,传染快受到人们的关注.而在这些经济贫困地区及时的公共健康教育是控制疾病的一种手段.基于此,本文研究了一类具有公共健康教育和饱和治疗率的随机潜蚤病模型的动力学行为.利用It?公式和构造Lyapunov函数等方法,首先证明了随机系统全局正解的存在唯一性;接着,分析了随机系统的正解围绕确定性系统的无病平衡点和地方病平衡点的渐近行为.最后,通过数值模拟验证了理论结果的正确性     

Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment

This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.     

The asymptotic behaviors of a stochastic social epidemics model with multi-perturbation

Alcohol abuse is a major social problem, which is often called social epidemic, for the some similarities to the classical infectious diseases. In this paper, we formulated a new stochastic alcoholism model based on the deterministic model proposed in \cite{Wangxy}, with the mortalities of all populations as well as the contact infected coefficient are all perturbed. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. Finally, we carry out numerical simulations to support our theoretical results.     

Bayesian prediction of crack growth based on a hierarchical diffusion model

A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd.     

The influence of forestry resources on rainfall: A deterministic and stochastic model

In this paper, we propose and analyze a deterministic model along with its stochastic version to address the problem of scanty rainfall by means of forestry resources. For deterministic model, boundedness of the system, feasibility of equilibria and their stability behavior are discussed. For stochastic model, boundedness, existence, uniqueness of global positive solution and sufficient conditions for the existence of unique stationary distribution are obtained. Model analysis reveals that the stability of the forest cover equilibrium state depends only on the model parameters in the deterministic case, however it also depends on the magnitude of the intensities of white noise terms in the stochastic case. To validate analytically obtained results and see the effect of key parameters, we have simulated proposed models using Indian annual rainfall data. The proposed model suggests that for the parameter values given in Table 2, the plantation of trees with slight higher intrinsic growth rate is beneficial to increase the rainfall.     

STOCHASTIC SIRS MODEL DRIVEN BY LVY NOISE

The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war,terrorism and others.First,adding random perturbations proportionally to each variable,we get the dynamic properties around the positive equilibrium of the deterministic model and the conditions for persistence and extinction.Second,giving a random disturbance to endemic equilibrium,we get a stochastic system with jumps.By modifying the existing Lyapunov function,we prove the positive solution of the system is stochastically stable.     

Exclusion and persistence in deterministic and stochastic chemostat models

We first introduce and analyze a variant of the deterministic single-substrate chemostat model. In this model, microbe removal and growth rates depend on biomass concentration, with removal terms increasing faster than growth terms. Using a comparison principle we show that persistence of all species is possible in this scenario. Then we turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation. In particular, we show that random effects may lead to extinction in scenarios where the deterministic model predicts persistence. On the other hand, we also establish some stochastic persistence results.     

Algorithm for the continuous estimation of a disturbance in a stochastic differential equation

Based on the approach of the theory of dynamic inversion, the problem of continuous estimation of an unknown deterministic disturbance in an Ito stochastic differential equation is investigated with the use of inaccurate measurements of the current phase state. An auxiliary model equation with a control approximating the unknown input is derived. The suggested solution algorithm is constructive; an estimate for its convergence rate is written explicitly.     

On Stochastic Extremum Seeking via Adaptive Perturbation–Demodulation Loop

In this paper, we propose a stochastic approximation algorithm for optimization of functions based on an adaptive extremum seeking method. The essence of this method is to approximate the gradient direction by introduction of a probing sequence, that is added to approximations and subsequently demodulated using an adaptive gain. Assuming that the probing and the demodulation signals are martingale difference sequences with adaptive diminishing gains, it is proved that the approximations converge almost surely to the optimizing value, under mild constraints on the measurement disturbance, and without assuming a priori boundedness of the approximation sequence. The measurement disturbance can contain a stochastic component, as well as a mean-square bounded deterministic component. The stochastic component can be nonstationary colored noise or a state-dependent random sequence.     

A dynamic stochastic version of the pitcher‐hamblin‐miller model of “collective violence"*

The central equation of the deterministic diffusion model of Pitcher, Hamblin, and Miller (1978) is formulated as a time‐inhomogeneous stochastic process. It will be shown that the stochastic process leads to a negative binomial distribution. The deterministic diffusion function can be derived from the stochastic model and is identical to the expected value as a function of time. Therefore the deterministic model is supported in terms of the underlying stochastic process. Moreover the stochastic model allows the prediction of the distribution for any point in time and the construction of prediction intervals.