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Abstract: Random impulsive differential equations (RIDEs) are a kind of mathematical models with extensive applications. In this paper, the Euler scheme for RIDEs is first brought forward, one of whose important applications is to generate the whole approximate trajectories of RIDEs. Thus the proposed Euler scheme allows us to approximate moments, functionals and the distribution for the underlying process and perform Monte-Carlo type analysis. The obtained results show that the Euler scheme is at least 1-order of step h when the right terms of equation satisfy Lipschitz conditions and the waiting times of random impulses follow the mutually independent exponential distribution with the same parameter λ. Thus it is an efficient method for numerical simulation. [Copyright &y& Elsevier]

In the paper, p-moment stability of stochastic differential equations with jumps is considered. First, some preliminary notes are given. Then, several theorems on p-moment stability of these equations are established using Liapunov function. At last, an example is present to show application of the obtained results. [Copyright &y& Elsevier]