Practical stability of stochastic delay evolution equations

In this paper we investigate the almost sure practical stability for a class of stochastic functional evolution equations. We establish some sufficient conditions based on the construction of appropriate Lyapunov functional. The abstract results are then applied to some illustrative examples.Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (España)Junta de Andalucí

Partial asymptotic stability of neutral pantograph stochastic differential equations with Markovian switching

In this paper, we investigate the partial asymptotic stability (PAS) of neutral pantograph stochastic differential equations with Markovian switching (NPSDEwMSs). The main tools used to show the results are the Lyapunov method and the stochastic calculus techniques. We discuss a numerical example to illustrate our main results

Practical exponential stability in mean square of stochastic partial differential equations

The main aim of this paper is to establish some criteria for the mean square and almost sure practical exponential stability of a nonlinear monotone stochastic partial differential equations

Practical asymptotic stability of nonlinear stochastic evolution equations

In this paper we establish some su cient conditions ensuring almost sure practical asymptotic stability with a non-exponential decay rate for solutions to stochastic evolution equations based on Lyapunov techniques

Ulam-Hyers-Rassias stability of neutral stochastic functional differential equations

In this paper, by using the Gronwall inequality, we show two new results on the UlamHyers and the Ulam-Hyers-Rassias stabilities of neutral stochastic functional differential equations. Two examples illustrating our results are exhibited

Practical exponential stability of impulsive stochastic functional differential equations

This paper is devoted to the investigation of the practical exponential stability of impulsive stochastic functional differential equations. The main tool used to prove the results is the Lyapunov-Razumikhin method which has proven very useful in dealing with stability problems for differential systems when the delays involved in the equations are not differentiable but only continuous. An illustrative example is also analyzed to show the applicability and interest of the main results.Fondo Europeo de Desarrollo RegionalMinisterio de Economía y CompetitividadJunta de Andalucí

Practical stability with respect to a part of variables of stochastic differential equations

In this paper, practical stability with respect to a part of the variables of nonlinear stochastic differential equations is studied. The analysis of the global practical uniform asymptotic stability, the global practical uniform pth moment exponential stability, as well as the global practical uniform exponential stability with respect to a part of the variables of SDEs are carried out by using the Lyapunov techniques. Some illustrative examples to show the usefulness of the stability with respect to a part of variables notion are also provided

β-Stability in q-th Moment of Neutral Impulsive Stochastic Functional Differential Equations with Markovian Switching

In this paper, we investigate the β-stability in q-th moment for neutral impulsive stochastic functional differential equations with Markovian switching (NISFDEwMS). Moreover, β-stability in q-th moment is studied by using the Lyapunov techniques and a new Razumikhin-type theorem to prove our result. Finally, we check the main result by a numerical example

Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results

η-stability of hybrid neutral stochastic differential equations with infinite delay

In this paper, we study the η-stability in q-th moment (η.s.q.m) of hybrid neutral stochastic differential equations with infinite delay (HNSDEID) using the Lyapunov tech niques and the method of M-matrix. Finally, we apply the main result to some examples