The Wong–Zakai theorem for dynamical systems with parametric Poisson white noise excitation

Abstract

The theorem of Wong and Zakai is applied to obtain a mathematical model for systems under random impulse excitation, in case that the excitation process tends to be delta-correlated. By means of the Wong–Zakai transformation, a class of reducible non-linear stochastic integro-differential equations is identified. Exact stationary probability density functions for reducible stochastic integro-differential equations are calculated.