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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]

By means of Liapunov's direct method coupled with Razumikhin technique some sufficient conditions for (uniform, uniform and globally asymptotic, uniformly globally asymptotic, and globally exponential) p-moment stability of the zero solution of functional differential equations with random impulses are presented, where the parameter λ(t) in (dV(t, x(t)))/dt is not required to be negative definite. Thus the obtained results are convenient to apply. [Copyright &y& Elsevier]