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ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

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Acta Mathematica Scientia 2010年第5期30卷 1481-1491页

作者：刘娟徐建成胡亦钧 College of mathematics and statistics Hubei Normal University School of mathematics and statistics Wuhan University

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.

关键词： Markov-dependent risk model dividend barrier Cerber-Shiu function integro-differential equation Laplace transform

Anti-synchronization of a new hyperchaotic system via small-gain theorem

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Chinese Physics B 2010年第10期19卷 151-157页

作者：肖剑 College of mathematics and statistics Chongqing University

Based on the small-gain theorem, the anti-synchronization between two identical new hyperchaotic systems is investigated, moreover, the general sufficient conditions to achieve anti-synchronization between the new hyperchaotic system and the new hyperchaotic Lorenz system are obtained via small-gain theorem. Numerical simulations are performed to verify and illustrate the analytical results.

关键词： hyperchaotic system anti-synchronization small-gain theorem

Inference for dependence competing risks from bivariate exponential model under generalized progressive hybrid censoring with partially observed failure causes

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Journal of Systems Engineering and Electronics 2019年第1期30卷 201-208页

作者： WANG Liang LI Huanyu MA Jin'ge School of mathematics and statistics Xidian University

Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information ***, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.

关键词： dependence competing risk generalized progressive hybrid censoring bivariate exponential distribution Bayesian inference.

Synchronization of noise-perturbed generalized Lorenz system by sliding mode control

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Chinese Physics B 2009年第1期18卷 91-97页

作者：孔翠翠陈士华 School of mathematics and statistics Wuhan University

Synchronization of a noise-perturbed generalized Lorenz system by using sliding mode control method is investigated in this paper. Two sliding mode control methods are proposed to synchronize the noise-perturbed gener... 详细信息

关键词： sliding mode control synchronization generalized Lorenz system

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

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Journal of Systems Science & Complexity 2018年第4期31卷 889-906页

作者： ZHOU Deqin MU Chunlai College of mathematics and statistics Chongqing University

This paper considers the Rosenau equation with a moving control δtu＋δtδx4u＋δxu＋uδzu=a（x＋ct）h（x,t）,c≠0,x∈T=R/（2πZ）,t〉0, The authors prove that the Rosenau equation with a moving control is locally exact controllable in H8（T） with s ≥ 0 and globally exponential stable in H8（T） with s ≥2. The two results nontrivially extend the work of （Rosier L and Zhang B Y, 2013） from the BBM equation to the Rosenau equation.

关键词： Exact controllability Rosenau equation stabilization

Stability analysis for semi-Markovian switched stochastic systems with asynchronously impulsive jumps

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Science China(Information Sciences) 2021年第1期64卷 162-174页

作者： Xiaowu MU Zenghui HU School of mathematics and statistics Zhengzhou University

The almost surely(a.s.) exponential stability is studied for semi-Markovian switched stochastic systems with randomly impulsive jumps. We start from the case that switches and impulses occur synchronously, in which the impulsive switching signal is a semi-Markovian process. For the case that switches and impulses occur asynchronously, the impulsive arrival time sequence and the types of jump maps are driven by a renewal process and a Markov chain, respectively. By applying the multiple Lyapunov function approach, sufficient conditions of exponential stability a.s. are obtained based upon the ergodic property of semi-Markovian process. The validity of the proposed theoretical results is demonstrated by a numerical example.

关键词： stochastic systems multiple Lyapunov function almost surely exponential stability impulsive jumps semi-Markovian switching renewal process

Uniformity Pattern of Asymmetric Fractional Factorials

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Journal of Systems Science & Complexity 2016年第2期29卷 499-510页

作者： QIN Hong WANG Zhenghong CHATTERJEE Kashinath Faculty of mathematics and statistics Central China Normal University School of mathematics and statistics South-Central University for Nationalities Department of statistics Visva-Bharati University

The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional *** the basis of Lee discrepancy,the authors define the projection Lee discrepancy to measure the uniformity for low-dimensional projection ***,the concepts of uniformity pattern and minimum projection uniformity criterion are proposed,which can be used to assess and compare two and three mixed levels *** justification of uniformity pattern is also investigated.

关键词： Lower bound minimum projection uniformity orthogonality projection Lee discrepancy uniformity pattern.

Statistical Diagnosis for HIV Dynamics Based on Mean Shift Outlier Model

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Journal of Systems Science & Complexity 2015年第3期28卷 592-605页

作者： WU Ting LIU Sanyang ZHOU Jie School of mathematics and statistics Xidian University

Ordinary differential equation(ODE) are widely used for quantifying HIV viral *** is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. In this study, the authors use the Mean Shift Outlier Model(MSOM) to detect outliers in HIV model based on the two-step estimation of ODE. Approximate formula for shift parameter is derived. Furthermore, a score test statistic is constructed and its approximating distribution is established. The simulation results show that: 1) The boundary points have more impact on the parameter estimation relative to interior points. 2) The proposed procedure can detect the outliers effectively. The authors illustrate the proposed approach using an application example from an HIV clinical trial and find similar pattern to the simulation studies.

关键词： HIV dynamics local polynomial smoothing mean shift outlier model nonparametric regression.

Controlled Mean-Field Backward Stochastic Differential Equations with Jumps Involving the Value Function

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Journal of Systems Science & Complexity 2016年第5期29卷 1238-1268页

作者： LI Juan MIN Hui School of mathematics and statistics Shandong University

This paper discusses mean-field backward stochastic differentiM equations （mean-field BS- DEs） with jumps and a new type of controlled mean-field BSDEs with jumps, namely mean-field BSDEs with jumps strongly coupled with the value function of the associated control problem. The authors first prove the existence and the uniqueness as well as a comparison theorem for the above two types of BSDEs. For this the authors use an approximation method. Then, with the help of the notion of stochastic backward semigroups introduced by Peng in 1997, the authors get the dynamic programming principle （DPP） for the value functions. Furthermore, the authors prove that the value function is a viscosity solution of the associated nonlocal Hamilton-Jacobi-Bellman （HJB） integro-partial differential equation, which is unique in an adequate space of continuous functions introduced by Barles, et al. in 1997.

关键词： Dynamic programming principle (DPP) Hamilton-Jacobi-Bellman (HJB) equation mean-field backward stochastic differential equation (mean-field BSDE) with jump Poisson random measure value function.