Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching

The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching. Linear NSDDEs with Markovian switching and nonlinear examples will be discussed to illustrate the theory.     

pth Moment stability of impulsive stochastic delay differential systems with Markovian switching

This paper is concerned with the pth moment stability of impulsive stochastic delay differential systems with Markovian switching. By using the Razumikhin-type method, some stability criteria are obtained, which can loosen the constraints of the existing results and thus reduce the conservativeness. Two examples are presented to demonstrate the usefulness of the proposed results.     

Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet. In the paper, the Euler–Maruyama method for neutral stochastic delay differential equations is developed. The key aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition.     

马尔可夫调制及带Poisson跳随机时滞微分方程依分布稳定

本文讨论马尔可夫调制及带Poisson跳随机时滞微分方程,其主要目的是研究方程解的依分布稳定.     

Comparison principle and stability criteria for stochastic differential delay equations with Markovian switching

In the present paper we first obtain the comparison principle for the nonlinear stochastic differential delay equations with Markovian switching. Later, using this comparison principle, we obtain some stability criteria, including stability in probability, asymptotic stability in probability, stability in thepth mean, asymptotic stability in the pth mean and the pth moment exponential stability of such equations. Finally, an example is given to illustrate the effectiveness of our results.     

广义中立型系统的渐近稳定性

讨论了广义中立型延迟系统理论的渐近稳定性,给出了广义中立型系统渐近稳定的一些充分条件。     

Approximate solutions of stochastic differential delay equations with Markovian switching

Recently, stochastic differential equations with Markovian switching (SDEwMS) have received a great deal of attention. In this paper, the Euler–Maruyama method is developed, one of the most powerful numerical schemes, for the stochastic differential delay equations with Markovian switching (SDDEwMS).     

The asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching and with polynomial growth

This paper discusses the asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching (SDSwMSs). The systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition. By applying some novel techniques, we propose some conditions under which such SDSwMSs are asymptotically stable and exponentially stable. Nontrivial examples are provided to illustrate our results.     

Comparison principle and stability of Ito stochastic differential delay equations with Poisson jump and Markovian switching

In this paper the comparison principle for the nonlinear Itô stochastic differential delay equations with Poisson jump and Markovian switching is established. Later, using this comparison principle, we obtain some stability criteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptotic stability in the pth mean and the pth moment exponential stability of such equations. Some known results are generalized and improved.     

Global stability of coupled nonlinear systems with Markovian switching

This paper investigates the global stability of a coupled nonlinear system with Markovian switching (CNSMS), which can be described in a graph. A theoretical framework for the construction of Lyapunov function for the CNSMS is derived in a combined method of graph theory and Lyapunov function. Furthermore, we obtain a global stochastic asymptotical stability principle, which has a close relation to the topology property of the graph. Finally, to illustrate the capabilities of the principle, the stochastic stability of a coupled oscillator system is investigated.     

Exponential estimates for stochastic delay hybrid systems with Markovian switching

This paper deals with the problem of norm bounds for the solutions of stochastic hybrid systems with Markovian switching and time delay.Based on Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality(LMI)approach,mean square exponential estimates for the solutions of this class of linear stochastic hybrid systems are derived.Finally,An example is illustrated to show the applicability and effectiveness of our method.     

Stability in distribution of neutral stochastic functional differential equations with Markovian switching

Stability in distribution of stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching have been studied by several authors and this kind of stability is an important property for stochastic systems. There are several papers which study this stability for stochastic differential equations with Markovian switching and stochastic differential delay equations with Markovian switching technically. In our paper, we are concerned with the general neutral stochastic functional differential equations with Markovian switching and we derive the sufficient conditions for stability in distribution. At the end of our paper, one example is established to illustrate the theory of our work.     

The stability of nonlinear neutral differential systems

In this paper, the author uses the method of inequality analysis to study the stability of nonlinear neutral differential systems. Some criteria for being exponentially stable in the large inC ₁ space are obtained.     

An analytic approximation of solutions of stochastic differential delay equations with Markovian switching

In this paper, we are concerned with the stochastic differential delay equations with Markovian switching (SDDEwMSs). As stochastic differential equations with Markovian switching (SDEwMSs), most SDDEwMSs cannot be solved explicitly. Therefore, numerical solutions, such as EM method, stochastic Theta method, Split-Step Backward Euler method and Caratheodory’s approximations, have become an important issue in the study of SDDEwMSs. The key contribution of this paper is to investigate the strong convergence between the true solutions and the numerical solutions to SDDEwMSs in the sense of the L^p-norm when the drift and diffusion coefficients are Taylor approximations.     

Oscillation criteria for third-order neutral differential equations with continuously distributed delay

The purpose of this paper is to study the oscillation of a certain class of third-order neutral differential equations with continuously distributed delay. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.     

Linear stability of general linear methods for systems of neutral delay differential equations

This paper is concerned with the numerical solution of delay differential equations (DDEs). We focus on the stability of general linear methods for systems of neutral DDEs with multiple delays. A type of interpolation procedure is considered for general linear methods. Linear stability properties of general linear methods with this interpolation procedure are investigated. Many extant results are unified.     

Stability of neutral stochastic functional differential equations with Markovian switching driven by G-Brownian motion

Little seems to be known about stability results on the neutral stochastic function differential equations with Markovian switching driven by G-Brownian (G-NSFDEwMSs). This paper aims at investigating the pth moment exponential stability for G-NSFDEwMSs to fill this gap. Some sufficient conditions on the pth moment exponential stability of the trivial solution are derived by employing the Razumikhin-type method, stochastic analysis, and algebraic inequality technique. Moreover, an example is provided to illustrate the effectiveness of the obtained results.     

中立型时滞系统的稳定性改进判据

研究了含有时变时滞的不确定中立系统的时滞相关稳定性问题.假定不确定参数是范数有界的,通过构造新的Lyapunov泛函和使用更一般的时滞分解方法,得到了基于LMI新颖的时滞相关稳定条件,并且用Matlab LMI工具箱很容易地求解.数值实例表明本文方法所得结果优于现有文献中的结果.