On The Stability For Stochastic Differential Equations And Random Impulsive Functional Differential Equations

In this dissertation we consider the stability of several stochastic diferential systems and functional diferential systems with impulsive effect on random moments, respectively. In Chapter 2, the methods used to study the stability and boundedness of the classical functional diferential equations is generalized to the Ito-stochastic functional diferential systems . Some sufficient conditions for uniform stability and the uniform aymptotic stability in terms of two measures are obtained.At the same time ,Some sufficient conditions for uniform boundedness and uniform boundedness and ultimate boundedness and uniform ultimate boundedness in terms of two measures are also obtained. As applications of our results ,we obtain the sufficient conditions for uniform P-stability and uniform asymptotic P-stability of the considered system ,and also obtain the sufficient conditions for uniform P-boundedness ,uniform P-boundedness and ultimate boundedness,and uniform ultimate P- boundedness,Some results are generalized and improved. In Chapter 3, we give the following Ito-stochastic differential systems with impulsive effect on random moments:we mainly study its stability and boundedness, obtain the sufficient conditions for uniform P-stability and uniform asymptotic P-stability of the considered system ,a the sufficient conditions for uniform P-boundedness , uniform P-boundedness and ultimate bounded-ness,and uniform ultimate P- boundedness ,then we give some examples to explain our results . In Chapter 4, we investigate the stability of the following stochastic differential systems with impulsive effect on random moments:, we obtain the stability criteria for the pth monment exponential stability of the considered systems . In Chapter 5 ,we discuss the stability of the stochastic differential system with Compensated Levy flow.First ,In §5.2,we give some sufficient conditions of Pth exponential stability and aimost surely exponential stability of the trivial solution to the stochastic functional differential system with Compensated Levy flow.Second ,In §5.3,we give some sufficient conditions of Pth exponential stability of the trivial solution to the stochastic differential system with Compensated Levy flow.Some results are generalized.In Chapter 6, we investigate the stability in terms of two measures of the trivial solution to the following model of nonlinear differential systems with impulsive effect on random moments :some sufficient conditions of stability in terms of two measures of the trivial solution to the considered systems,in which (dV(t,x(t)))/(dt) isn't required to be negtive definite . In Chapter 7,we give an improved the following model :By using comparision pricinple and Liapunov function ,we obtained the conditions for uniform eventual stability ,asymptotic eventual stability of the trivial solution to the considered systems.