This paper focuses on the problem of pth moment and almost sure exponential stability impulsive neutral stochastic functional differential equations (INSFDEs). Based Lyapunov function average dwell time (ADT), two sufficient criteria for INSFDEs are derived, which manifest that result obtained in this is more convenient to be used than those Razumikhin conditions former literature. Finally, num...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

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In this paper, we discuss a new type of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and ...

This article concerns the behavior of the solutions to periodic linear neutral delay differential equations as well as to periodic linear neutral delay difference equations. Some new results are obtained via two appropriate distinct roots of the corresponding (so called) characteristic equation.

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

So far there are not many results on the attractor for the solutions of stochastic differential delay equations. The main aim of this paper is to establish new results on the attractor, from which follow several new criteria on the almost surely asymptotic stability for stochastic differential delay equations. As another by product, a number of new criteria on the boundedness of the solutions a...