Response of Duffing system with delayed feedback control under combined harmonic and real noise excitations

This paper presents a procedure for predicting the response of Duffing system with delayed feedback bang–bang control under combined harmonic and real noise excitations by using the stochastic averaging method. First, the time-delayed feedback bang–bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker–Plank–Kolmogorov (FPK) equation associated with the averaged Itô equations. It is shown that the time delay in feedback control can deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing system. The validity of the proposed method is confirmed by digital simulation.     

Stochastic stability of Duffing–Mathieu system with delayed feedback control under white noise excitation

The asymptotic Lyapunov stability with probability one of Duffing–Mathieu system with time-delayed feedback control under white-noise parametric excitation is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method and the expression for the Lyapunov exponent of the linearized averaged Itô equations is derived. Finally, the effects of time delay in feedback control on the Lyapunov exponent and the stability of the system are analyzed. Meanwhile, the stability conditions for the system with different time delays are also obtained. The theoretical results are well verified through digital simulation.     

Stochastic models for air cargo terminal manpower supply planning in long‐term operations

In this research, based on two deterministic‐demand planning models, we established two long‐term stochastic‐demand planning models by incorporating the stochastic disturbances of manpower demands that occur in actual operations. The models are formulated as mixed integer linear programs that are solved using a mathematical programming solver. To compare the performance of the two stochastic‐demand and two deterministic‐demand planning models under the stochastic demands that occur in actual operations, we further develop a simulation‐based evaluation method. Finally, we perform numerical tests using real operating data from a Taiwan air cargo terminal. The preliminary results show that the stochastic models could be useful for planning air cargo terminal manpower supply. Copyright © 2008 John Wiley & Sons, Ltd.     

不同风险偏好下虚拟企业风险规划研究

针对虚拟企业风险规划问题,在分析其各种风险具有随机性的特点的基础上,运用随机规划理论,分别建立风险规划的期望值模型和机会约束规划模型来描述决策者在不同风险偏好下的决策行为。针对所建立的模型,分别设计了基于蒙特卡罗模拟的粒子群优化算法、遗传算法和蚁群算法对其进行求解。仿真分析表明期望值模型较好地描述了风险中性决策者的决策行为,机会约束规划模型随着其偏好系数取值的不同描述了不同风险偏好(风险厌恶、风险中性、风险爱好)决策者的决策行为。通过对三种算法仿真结果的比较分析,表明基于蒙特卡罗模拟的粒子群优化算法在寻优能力、稳定性和收敛速度等方面优于其余两种算法,是解决此类风险规划问题的有效手段。     

Long term behaviors of stochastic single-species growth models in a polluted environment II

This is a continuation of our paper [M. Liu, K. Wang, X. Liu. Long term behaviors of stochastic single-species growth models in a polluted environment. Appl Math Model 2011;35:752–62]. This work still devotes to studying three stochastic single-species models in a polluted environment. For the first system, sufficient criteria for extinction, stochastic non-persistence in the mean, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence of the population are established. The threshold between stochastic weak persistence in the mean and extinction is obtained. For the second model, sufficient conditions for extinction, stochastic non-persistence in the mean, stochastic weak persistence, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence are established. The threshold between stochastic weak persistence and extinction is derived. For the third system, the threshold between stochastic weak persistence and extinction is obtained.     

Two-stage least squares based iterative estimation algorithm for CARARMA system modeling

For stochastic systems described by the controlled autoregressive autoregressive moving average (CARARMA) models, a new-type two-stage least squares based iterative algorithm is proposed for identifying the system model parameters and the noise model parameters. The basic idea is based on the interactive estimation theory and to estimate the parameter vectors of the system model and the noise model, respectively. The simulation results indicate that the proposed algorithm is effective.     

Stochastic modeling of carcinogenesis by state space models: a new approach

In this paper, we have developed some state space models for carcinogenesis involving multievent models and multiple pathways models. In these state space models, the stochastic system models are stochastic models of carcinogenesis expressed in terms of stochastic differential equations, whereas the observation models are statistical models based on the observed number of detectable preneoplastic lesions per individual over time and the observed number of detectable cancer tumors per individual over time. In this paper, we have applied some of the theories to some animal papillomas data from some initiation-promotion experiments on skin cancer in mice to estimate some unknown parameters. For this data set we have obtained excellent fit by a model with three piece-wise intervals.     

Curved exponential families of stochastic processes and their envelope families

Exponential families of stochastic processes are usually curved. The full exponential families generated by the finite sample exponential families are called the envelope families to emphasize that their interpretation as stochastic process models is not straightforward. A general result on how to calculate the envelope families is given, and the interpretation of these families as stochastic process models is considered. For Markov processes rather explicit answers are given. Three examples are considered some in detail: Gaussian autoregressions, the pure birth process and the Ornstein-Uhlenbeck process. Finally, a goodness-of-fit test for censored data is discussed.     

Probabilistic verification of a biodiesel production system using statistical model checking

Biochemical system designers are increasingly using formal modelling, simulation, and verification methods to improve the understanding of complex systems. Probabilistic models can incorporate realistic stochastic dynamics, but creating and analysing probabilistic models in a formal way is challenging. In this work, we present a stochastic model of biodiesel production that incorporates an inexpensive test of fuel quality, and we validate the model using statistical model checking, which can be used to evaluate simple or complex temporal properties efficiently. We also describe probabilistic simulation and analysis techniques for stochastic hybrid system (SHS) models to demonstrate the properties of our model. We introduce a variety of properties for various configurations of the reactor as well as results of testing our model against the properties.     

Modeling of degradation data via wiener stochastic process based on acceleration factor constant principle

This paper proposes a systematic method of modeling accelerated degradation data based on the acceleration factor constant principle. Wiener stochastic process is considered because it is the most extensively used for degradation modeling. For the Wiener stochastic processes with three different time functions, the parameter relationships, which should be satisfied under any two different stress levels, are deduced according to the acceleration factor constant principle. The deduced parameter relationships indicate the stress-related parameters, which are applied to establish accurate accelerated degradation models. In addition, the deduced parameter relationships provide a guidance to test the consistency of the degradation mechanisms under different stress levels. A hypothesis method based on Analysis of Variance is adopted to identify the accelerated stress levels with different degradation mechanism. The degradation data under these stress levels should not be used to assess the product's reliability. The methods of validating accelerated degradation models and reliability assessments are also proposed. The simulation results prove the feasibility and effectiveness of the proposed methods. From the numerical example, it is concluded that the accelerated degradation model established based on the acceleration factor constant principle is more credible and accurate.     

A stochastic Lagrangian representation of the three‐dimensional incompressible Navier‐Stokes equations

In this paper we derive a probabilistic representation of the deterministic three‐dimensional Navier‐Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self‐contained proof of local existence for the nonlinear stochastic system and can be extended to formulate stochastic representations of related hydrodynamic‐type equations, including viscous Burgers equations and Lagrangian‐averaged Navier‐Stokes alpha models. © 2007 Wiley Periodicals, Inc.     

稀疏过程在保险公司破产问题中的应用

本文讨论适用于一类人寿保险和财产保险的风险过程 ,其中保单到达服从Poisson过程 ,而描述索赔发生的计数过程为保单到达过程的 p -稀疏过程。对此模型给出了破产概率的上界并对该上界进行了随机模拟 ,同时把所得结果与经典情形进行比较     

基于价格均值回复与随机波动率的信用差价衍生产品定价

为了研究均值回复特征与随机波动率对金融衍生品定价的影响,考虑状态变量的均值回复特征与两种随机波动率过程:平方根过程与O rnste in-U h lenbeck过程,应用解偏微分与特征函数方法,分析衍生品的定价方程,推导出基于均值回复特征与随机波动率的信用差价期权、信用差价上限与下限的定价公式.结果表明,均值回复和随机波动率在衍生品定价中起重要影响.     

State-space stochastic volatility models: A review of estimation algorithms

Stochastic volatility models (SVMs) represent an important framework for the analysis of financial time series data, together with ARCH-type models; but unlike the latter, the former, at least from the statistical point of view, cannot rely on the possibility of obtaining exact inference, in particular with regard to maximum likelihood estimates for the parameters of interest. For SVMs, usually only approximate results can be obtained, unless particularly sophisticated estimation strategies like exact non-gaussian filtering methods or simulation techniques are employed. In this paper we review SVM and present a new characterization for them, called ‘generalized bilinear stochastic volatility’. © 1996 John Wiley & Sons, Ltd.     

Persistence and extinction in stochastic non-autonomous logistic systems

This paper studies two widely used stochastic non-autonomous logistic models. For the first system, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The critical number between weak persistence and extinction is obtained. For the second system, sufficient criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and stochastic permanence are established. The critical number between weak persistence in the mean and extinction is obtained. It should be pointed out that this research is systematical and complete. In fact, the behaviors of the two models in every coefficient cases are cleared up by the results obtained in this paper.     

Stochastic actor‐oriented models for network change

A class of models is proposed for longitudinal network data. These models are along the lines of methodological individualism: actors use heuristics to try to achieve their individual goals, subject to constraints. The current network structure is among these constraints. The models are continuous time Markov chain models that can be implemented as simulation models. They incorporate random change in addition to the purposeful change that follows from the actors’ pursuit of their goals, and include parameters that must be estimated from observed data. Statistical methods are proposed for estimating and testing these models. These methods can also be used for parameter estimation for other simulation models. The statistical procedures are based on the method of moments, and use computer simulation to estimate the theoretical moments. The Robbins‐Monro process is used to deal with the stochastic nature of the estimated theoretical moments. An example is given for Newcomb's fraternity data, using a model that expresses reciprocity and balance.     

First-passage failure of linear oscillator with non-classical inelastic impact

The first-passage failure of linear oscillator with inelastic impact subjected to the additive and multiplicative random noises is investigated. The impact is described by the non-classical inelastic impact model, which is essentially different from the traditional impact model and can provide the whole information of the impact process. First of all, the impact force in the motion equation is replaced by the quasi-linear damping and nonlinear stiffness terms. Then, the stochastic averaging is adopted and the averaged Itô stochastic deferential equation of the total system energy is derived. Last, by solving the established backward Kolmogorov equation and Pontryagin equation from the averaged Itô equation numerically, the conditional reliability, the conditional probability density function (PDF) and the mean time of first-passage failure can be obtained. The comparison between the analytical results and those from Monte-Carlo simulation reveals the proposed procedure is effective. The influences of some system parameters are discussed in detail.     

Approximative solution of the coagulation–fragmentation equation by stochastic particle systems

This paper studies stochastic particle systems related to the coagulation fragmentation equation. For a certain class of unbounded coagulation kernels and fragmentation rates, relative compactness of the stochastic systems is established and weak accumulation points are characterized as solutions. These results imply a new existence theorem. Finally a simulation algorithm based on the particle systems is proposed     

Stochastic portfolio specific mortality and the quantification of mortality basis risk

In the last decade a vast literature on stochastic mortality models has been developed. However, these models are often not directly applicable to insurance portfolios because:

(a) For insurers and pension funds it is more relevant to model mortality rates measured in insured amounts instead of measured in the number of policies.

(b) Often there is not enough insurance portfolio specific mortality data available to fit such stochastic mortality models reliably.

Therefore, in this paper a stochastic model is proposed for portfolio specific mortality experience. Combining this stochastic process with a stochastic country population mortality process leads to stochastic portfolio specific mortality rates, measured in insured amounts. The proposed stochastic process is applied to two insurance portfolios, and the impact on the Value at Risk for longevity risk is quantified. Furthermore, the model can be used to quantify the basis risk that remains when hedging portfolio specific mortality risk with instruments of which the payoff depends on population mortality rates.     

Stochastic Lotka–Volterra systems with Lévy noise

This paper is concerned with stochastic Lotka–Volterra models perturbed by Lévy noise. Firstly, stochastic logistic models with Lévy noise are investigated. Sufficient and necessary conditions for stochastic permanence and extinction are obtained. Then three stochastic Lotka–Volterra models of two interacting species perturbed by Lévy noise (i.e., predator–prey system, competition system and cooperation system) are studied. For each system, sufficient and necessary conditions for persistence in the mean and extinction of each population are established. The results reveal that firstly, both persistence and extinction have close relationships with Lévy noise; Secondly, the interaction rates play very important roles in determining the persistence and extinction of the species.