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

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