共查询到20条相似文献,搜索用时 15 毫秒
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Abstract The classical Khasminskii theorem (see [6]) on the nonexplosion solutions of stochastic differential equations (SDEs) is very important since it gives a powerful test for SDEs to have nonexplosion solutions without the linear growth condition. Recently, Mao [13] established a Khasminskii-type test for stochastic differential delay equations (SDDEs). However, the Mao test can not still be applied to many important SDDEs, e.g., the stochastic delay power logistic model in population dynamics. The main aim of this paper is to establish an even more general Khasminskii-type test for SDDEs that covers a wide class of highly nonlinear SDDEs. As an application, we discuss a stochastic delay Lotka-Volterra model of the food chain to which none of the existing results but our new Khasminskii-type test can be applied. 相似文献
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本文采用了一例特定的Lyapunov函数,来研究带Markov调制的随机微分延迟方程的p阶指数稳定性,并对其几乎必然指数稳定性也进行了探讨. 相似文献
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Chenggui Yuan 《随机分析与应用》2013,31(6):1259-1276
Abstract In this paper, we investigate the stability in terms of two measures for stochastic differential equations with Markovian switching by using the method of Lyapunov functions. Our new theory can not only be used to show a given system to be stochastically stable in the classical sense, but can also be used to deal with some situations where the classical stability theory is not applicable. 相似文献
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随机微分延迟方程的指数稳定性被人们广泛研究,但讨论带Markov调制的随机微分延迟方程的函数稳定性的不多.本文主要研究了两种类型的函数稳定性.我们采用了一例特定的Lyapunov函数,来研究带Markov调制的随机微分延迟方程的p阶矩ψα-函数稳定性,并对其几乎必然ψβ/p-函数稳定性也进行了探讨. 相似文献
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The main aim of this article is to deal with the almost-sure stability of stochastic differential delay equations. Our improved theorems give better results while conditions imposed on the Lyapunov function are much weaker, thus, it is easier to find a right Lyapunov function in application. 相似文献
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《随机分析与应用》2013,31(3):737-751
In this paper, we shall use multiple Lyapunov functions to establish some sufficient criteria for locating the limit sets of solutions of stochastic differential equations with respect to semimartingales. From them follow many useful results on stochastic asymptotic stability and boundedness, including some classical results as special cases. In particular, our new asymptotic stability criteria do not require the diffusion operator associated with the underlying stochastic differential equation be negative definite, while most of the existing results do require this negative definite property essentially. 相似文献
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Abstract In this paper, we will establish new results on the attraction for solutions to stochastic functional differential equations with respect to semimartingale. Most of the existing results stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in the study of attraction. Moreover, from our results on the attraction follow several new criteria on almost surely asymptotic stability and boundedness of the solutions. 相似文献
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Abstract In this article the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their 𝕃 p -consistency, numerical 𝕃 p -stability and 𝕃 p -convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency. 相似文献
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In this paper, we introduce a stochastic integral with respect to the solution X of the fractional heat equation on [0,1], interpreted as a divergence operator. This allows to use the techniques of the Malliavin calculus in order to establish an Itô-type formula for the process X. 相似文献
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尽管具有马尔科夫切换型随机微分方程的稳定性受到了人们的关注,但是关于具有马尔科夫切换型中立型随机泛函微分方程的稳定性的研究则很少.本文的主要目的是试图研究这一问题,我们证明了解的存在唯—性,并得到了p-阶指数稳定性和几乎处处指数稳定性的判据. 相似文献
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In this paper, we investigate the existence and uniqueness of solutions to stochastic differential delay equations under a local Lipschitz condition but without linear growth condition on its coefficients. Moreover, we prove convergence in probability of the Euler–Maruyama approximation as well as of the stochastic theta method approximation to the exact solution. 相似文献
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本文研究带Poisson跳和Markovian调制的中立型随机微分方程的数值解的收敛性质.用数值逼近方法求此微分方程的解,并证明了Euler近似解在此线性增长条件和全局Lipschitz条件更弱的条件下仍均方收敛于此方程的解析解. 相似文献
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This article studies the asymptotic behavior of a stochastic Chemostat model with Lotka–Volterra food chain in which the dilution rate was influenced by white noise. The long-time behavior of the model is studied. Using Lyapunov function and Itô's formula, we show that there is a unique positive solution to the system. Moreover, the sufficient conditions for some population dynamical properties including the boundedness in mean and the stochastically asymptotic stability of the washout equilibrium were obtained. Furthermore, we show how the solutions spiral around the predator-free equilibrium and the positive equilibrium of deterministic system. Besides, the existence of the stationary distribution is proved for the considered model. Numerical simulations are introduced finally to support the obtained results. 相似文献