STOCHASTIC INTEGRODIFFERENTIAL AND DIFFERENTIAL-EQUATIONS OF NONLINEAR-SYSTEMS EXCITED BY PARAMETRIC POISSON PULSES

The connection between stochastic integro-differential equation and st ochastic differential equation of non-linear systems driven by paramet ric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of ext ernal excitation. In the case of parametric type excitation the two fo rmulation are equivalent if the non-linear argument in the integral re presentation is related by means of a series to the corresponding non- linear parametric term in the stochastic differential equation. Differ ential rules for the two representations to find moment equations of e very order of the response are also compared. (C) 1997 Elsevier Scienc e Ltd.