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1.
In this paper, we initiate a study on stochastic neutral partial functional differential equations in a real separable Hilbert space. Our goal here is to study the existence and uniqueness of a mild solution of this class of equations and also the exponential stability of the moments of a mild solution as well as its sample paths. The results obtained here generalize the main results from [Taniguchi, Stochastics and Stochastics Reports, 53, (1995) 41–52], [Taniguchi, Stochastic Analysis and Applications, 16, (1998) 965–975] and [Liu and Truman, Statistics Probability Letters, 50, (2000) 273–278]. An example is given to illustrate the theory.  相似文献   

2.
In this work, we investigate stochastic partial differential equations with variable delays and jumps. We derive by estimating the coefficients functions in the stochastic energy equality some sufficient conditions for exponential stability and almost sure exponential stability of energy solutions, and generalize the results obtained by Taniguchi [T. Taniguchi, The exponential stability for stochastic delay partial differential equations, J. Math. Anal. Appl. 331 (2007) 191-205] and Wan and Duan [L. Wan, J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory, Statist. Probab. Lett. 78 (5) (2008) 490-498] to cover a class of more general stochastic partial differential equations with jumps. Finally, an illustrative example is established to demonstrate our established theory.  相似文献   

3.
The fixed-point theory is first used to consider the stability for stochastic partial differential equations with delays. Some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given. These conditions do not require the monotone decreasing behavior of the delays, which is necessary in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763; Ruhollan Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, Stoch. Anal. Appl. 21 (2003) 161-181]. Even in this special case, our results also improve the results in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763].  相似文献   

4.
The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on paper [X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (2) (1997) 389-401], referring to mean square and almost sure exponential stability.  相似文献   

5.
A strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. The Razumikhin–Lyapunov type function methods and comparison principles are studied in pursuit of sufficient conditions for the moment exponential stability and almost sure exponential stability of equations in which we are interested. The results of [A.V. Svishchuk, Yu.I. Kazmerchuk, Stability of stochastic delay equations of Itô form with jumps and Markovian switchings, and their applications in finance, Theor. Probab. Math. Statist. 64 (2002) 167–178] are generalized and improved as a special case of our theory.  相似文献   

6.
In this article, we initiate a study on neutral stochastic functional evolution equations driven by jumps modulated by Markovian switching in real separable Hilbert spaces. Our goal here is to derive the existence and uniqueness of mild solutions to equations of this class under local non-Lipschitz condition proposed by Taniguchi [J. Math. Anal. Appl. 340:(2009)197–208] by means of stopping time technique and Banach fixed-point theorem. The results obtained here generalize the main results from Luo and Taniguchi [Stoch. Dyn. 9:(2009)135–152] and Jiang and Shen [Comput. Math. Appl. 61:(2011)1590–1594]. Finally, an example is worked out to illustrate the obtained results.  相似文献   

7.
本文主要运用Picard迭代和算子分数次幂方法,讨论了随机时滞偏微分方程适度解的存在性与唯一性,并对解的渐近性态进行了研究.这里方程的系数不满足Lipschitz条件,时滞r>0为有限的.最后给出了一个非Lipschitz条件的例子.  相似文献   

8.
In this paper, we investigate the pth moment and almost sure exponential stability of impulsive stochastic functional differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Meanwhile, an example and simulations are given to show that impulses play an important role in pth moment and almost sure exponential stability of stochastic functional differential equations with finite delay.  相似文献   

9.
In this paper, we study the piecewise pseudo almost periodicity in distribution for a stochastic process. Using the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we obtain the existence and the exponential stability of piecewise pseudo almost periodic in distribution mild solutions for impulsive partial neutral stochastic functional differential equations under non-Lipschitz conditions. Moreover, an example is given to illustrate the general theorems.  相似文献   

10.
In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results.  相似文献   

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