Qualitative Analysis On Differential Equations With Random Impulses

Impulsive differential systems have greatly extensive application. In this thesis, by Liapunov direct method coupled with Razumikhin technique, some sufficient conditions for p-moment stability of the zero solution to functional differential equations with random impulses are presented. Then, the existence and uniqueness in mean square of solutions to stochastic differential equations with random impulses are considered using Pearson's iteration and some stochastic analysis. At last, the Euler scheme for a class of stochastic differential equations with random impulses is offered, and then its continuous dependence on initial value and convergence are studied. It is proved that the Euler scheme is convergent with at least 1/2 order.