Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations
نویسندگان
چکیده
In this paper we shall discuss the almost sure exponential stability for a neutral differential difference equation with damped stochastic perturbations of the form d[x(t) −G(x(t − τ ))] = f(t, x(t), x(t − τ ))dt + σ(t)dw(t). Several interesting examples are also given for illustration. It should be pointed out that our results are even new in the case when σ(t) ≡ 0, i.e. for deterministic neutral differential difference equations.
منابع مشابه
Almost sure exponential stability of stochastic reaction diffusion systems with Markovian jump
The stochastic reaction diffusion systems may suffer sudden shocks, in order to explain this phenomena, we use Markovian jumps to model stochastic reaction diffusion systems. In this paper, we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps. Under some reasonable conditions, we show that the trivial solution of stocha...
متن کاملStability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...
متن کاملThe Exponential Stability of Neutral Stochastic Delay Partial Differential Equations
In this paper we analyse the almost sure exponential stability and ultimate boundedness of the solutions to a class of neutral stochastic semilinear partial delay differential equations. This kind of equations arises in problems related to coupled oscillators in a noisy environment, or in viscoeslastic materials under random or stochastic influences.
متن کاملSample Path Exponential Stability of Stochastic Neutral Partial Functional Differential Equations
In this paper, we study the almost sure moment exponential stability of mild solutions of stochastic neutral partial functional differential equations in real separable Hilbert spaces using local Lipschitz conditions. Even in the special case, when the neutral term is zero, the results obtained here appear to be new and complement the study in [Taniguchi, et al, J. Differential Eqns. 181 (2002)...
متن کاملRazumikhin-type Theorems on Exponential Stability of Neutral Stochastic Functional Differential Equations
Recently, we initiated in [Systems Control Lett., 26 (1995), pp. 245–251] the study of exponential stability of neutral stochastic functional differential equations, and in this paper, we shall further our study in this area. We should emphasize that the main technique employed in this paper is the well-known Razumikhin argument and is completely different from those used in our previous paper ...
متن کامل