Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise

In this study stochastic analysis of non-linear dynamical systems under ?-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ?-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained<br />considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ?/2-stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ?/2-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ?-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.