M. Dipaola et M. Vasta, STOCHASTIC INTEGRODIFFERENTIAL AND DIFFERENTIAL-EQUATIONS OF NONLINEAR-SYSTEMS EXCITED BY PARAMETRIC POISSON PULSES, International journal of non-linear mechanics, 32(5), 1997, pp. 855-862
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.