随机非线性物价模型的最优控制

将政府对价格系统的宏观调控作为外部控制力,建立受控的随机非线性物价模型;利用拟Hamilton系统随机平均法和随机动态规划原理的非线性随机控制策略对系统实施最优控制,控制目标是实现系统的稳定性变大;并通过对比控制前后的Lyapunov指教值说明了控制的有效性.     

A nonrandom lyapunov spectrum for nonlinear stochastic dynamical systems

We present a nonrandom version of the Multiplicative Ergodic (Oseledec) Theorem for a nonlinear stochastic dynamical system on a smooth compact Riemannian Manifold M. This theorem characterises the a.s. asymptotic behaviour of the derivative system. Our approach (based on work of Furstenberg and Kifer, who deal with a linear system) is to consider an associated system on the projective bundle over M and to relate the behaviour of the theorem to the ergodic behaviour of this system. When the system has no random element, our work reduces to an alternative approach to the Multiplicative Ergodic Theorem for a diffeomorphism of M.     

Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics

A nonlinear stochastic dynamical model on a typical HAB algae diatom and dianoflagellate densities was created and presented in this paper. Simplifying the model through a stochastic averaging method, we obtained a two-dimensional diffusion process of averaged amplitude and phase. The singular boundary theory of diffusion process and the invariant measure theory were applied in analyzing the bifurcation of stability and the Hopf bifurcation of the stochastic system. The critical value of the stochastic Hopf bifurcation parameter was obtained and the conclusion that the position of Hopf bifurcation drifting with the parameter increase is presented as a result.     

The stochastic EOQ model with random sales price

The article deals with a stochastic economic order quantity (EOQ) model over a finite time horizon where uniform demand over the replenishment period is price dependent. The selling price is assumed to be a random variable that follows a probability density function. As demand is probabilistic, stock out situation may occur. Based on the partial backlogging and lost sale cases during stock out period, the author develops the criterion for the optimal solution for the replenishment size such that the integrated expected profit is maximized. Moreover, the article suggests a new function regarding price dependent demand. Finally, numerical examples and its sensitivity analysis of key parameters are given to illustrate the proposed model.     

一类随机细粒棘球蚴病传播动力学模型的研究

研究了一类具有随机环境波动和时滞的细粒棘球蚴病传播动力学模型,证明了在感染再生数R_01和噪声强度阈值R_0~N1时,感染平衡点E~*是依概率稳定的.探讨了环境噪声和时滞对控制细粒棘球蚴病传播的影响.     

A variational approach to stochastic nonlinear diffusion problems with dynamical boundary conditions

We study a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise; we allow stochastic boundary conditions that depend on the time derivative of the solution on the boundary. This work provides the existence and uniqueness of the solution and it shows the existence of an ergodic invariant measure for the corresponding transition semigroup; furthermore, under suitable additional assumptions, uniqueness and strong asymptotic stability of the invariant measure are proved.     

A nonlinear stochastic growth model on discrete time domains

In this paper, we introduce nonlinear stochastic dynamic problems on discrete time domains where events may occur at unevenly spaced time points. We define Euler equation and transversality condition for the problem. We prove that the Euler equation and the transversality condition are sufficient for the existence of the optimal solution. Next we generalize discrete time Cagan type rational expectation model to multivariate case. As an application of the main results, we obtain an explicit solution to a log-linearized nonlinear stochastic growth model.     

Simulation of a nonlinear stochastic ecology model

A nonlinear ecological system model is formulated as a stochastic process. The formulation traces a chemical nutrient as it undergoes random exchanges between the phytoplankton, the zooplankton, and the euphotic zone of an aquatic ecosystem. The Chapman-Kolmogorov equations are derived, and simulation techniques are used to study both single realizations and the statistical parameters which govern the system.     

一个基于Sidrauski宏观经济动力学模型的分析

Abstract. This paper formulates a kind of dynamical macro-economic model based onSidrauski‘s work,then presents the sufficient and necessary conditions of the stability of modelat equilibrium states ,and shows some results for special production functions.     

On a class of nonlinear stochastic dynamical systems: Analysis of the transient behaviour

A class of nonlinear dynamical systems with random parameters and initial conditions is considered. The transient time evolution of the mean value of the dependent variable is analyzed both by means of the stochastic averaging method and by Adomian's decomposition method. A proof of the equivalence of the decomposition method to the time series approximation of the dynamical response is provided. An application is made to the Van der Pol equation and finally a comparison between the two previously discussed methods is given.     

Concerning a stochastic dynamical system

We study the discrete-time dynamical system $$X_{n + 1} = 2\sigma \cos (2\pi \theta _n )g(X_n ), n \in \mathbb{Z},$$ Whereθ _n is an ergodic stationary process whose univariate distribution is uniform on the interval [0, 1], the functiong(x) is odd, bounded, increasing, and continous, and ? is the ring of integers. It is proved that under certain conditions there exists a unique stationary process that is a solution of the above equation and this process has a continous purely singular spectrum.     

Perturbed linear stochastic dynamical systems

This paper is concerned with a class of stochastic differential equations which arises by adding a nonlinear term involving a small parameter δ to the drift coefficient of a linear stochastic system. First, a stochastic representation of the solutions of a certain class of Cauchy problems is studied. Second, a finite time expansion in powers of δ of the expectations of functions is established. Third, the corresponding ergodic expansions are sought with additional assumptions regarding the existence of a unique ergodic measure.     

On a stochastic differential equation arising in a price impact model

We provide sufficient conditions for the existence and uniqueness of solutions to a stochastic differential equation which arises in the price impact model developed by Bank and Kramkov (2011)  and . These conditions are stated as smoothness and boundedness requirements on utility functions or Malliavin differentiability of payoffs and endowments.     

Parameter and moment bounds for a nonlinear stochastic ecology model

A differential equation model of a marine ecosystem is formulated as a stochastic process. The ecosystem is modeled by considering the random exchange of a chemical nutrient between three components of the ecosystem. The Chapman-Kolmogorov equations and the moment or cumulant generating functions for the process are derived to examine analytically the behavior of the moments of the process. Through the use of differential inequalities, bounds on the exchange rate parameters are derived to reflect component extinction. Bounds on the moments of the process are also obtained.     

A dynamical system for the approximate moments of nonlinear stochastic models of spiking neurons and networks

We consider multidimensional systems of coupled nonlinear stochastic differential equations suitable for the study of the dynamics of collections of interacting noisy spiking neurons. Assumptions based on the smallness of third and higher central order moments of membrane potentials and recovery variables are used to derive a system of ordinary differential equations for the approximate means, variances, and covariances. We show the usefulness of such a derivation for different cases of model neurons under the action of white noise currents.     

Inventory model with stochastic lead-time and price dependent demand incorporating advance payment

Inventory model for an item is developed in stochastic environment with price-dependent demand over a finite time horizon. Here, probabilistic lead-time is considered and shortages are allowed (if occurs). In any business, placement of an order is normally connected with the advance payment (AP). Again, depending upon the amount of AP, unit price is quoted, i.e., price discount is allowed. Till now, this realistic factor is overlooked by the researchers. In this model, unit price is inversely related with the AP amount. Against this financial benefit, the management has to incur an expenditure paying interest against AP. Taking these into account, mathematical expression is derived for the expected average profit of the system. A closed form solution to maximize the expected average profit is obtained when demand is constant. In other cases model is solved using generalized reduced gradient (GRG) technique and stochastic search genetic algorithm (GA). Moreover, results of the models without and with advance payment are presented and solved. The numerical examples are presented to illustrate the model and the results for two models obtained from two methods are compared in different cases. Also, some parametric studies and sensitivity analyses have been carried out to illustrate the behavior of the proposed model. It is observed that advance payment has positive effect on the system.     

Moment equations and Hermite expansion for nonlinear stochastic differential equations with application to stock price models

Exact moment equations for nonlinear Itô processes are derived. Taylor expansion of the drift and diffusion coefficients around the first conditional moment gives a hierarchy of coupled moment equations which can be closed by truncation or a Gaussian assumption. The state transition density is expanded into a Hermite orthogonal series with leading Gaussian term and the Fourier coefficients are expressed in terms of the moments. The resulting approximate likelihood is maximized by using a quasi Newton algorithm with BFGS secant updates. A simulation study for the CEV stock price model compares the several approximate likelihood estimators with the Euler approximation and the exact ML estimator (Feller, in Ann Math 54: 173–182, 1951).     

Stability analysis of a stochastic logistic model with nonlinear diffusion term

This paper presents an asymptotic analysis of a stochastic logistic population model with nonlinear diffusion term. The classical probability method is applied to obtain the criteria of asymptotic behavior for the considered model. The numerical simulations validate the efficiency of the theory analysis.