Stochastic response of linear and non-linear systems to alpha-stable Lévy white noises

The stochastic response of linear and non-linear systems to external α-stable Lévy white noises is investigated. In the literature, a
differential equation in the characteristic function (CF) of the response has been recently derived for scalar systems only, within the theory of
the so-called fractional Einstein–Smoluchowsky equations (FESEs). Herein, it is shown that the same equation may be built by rules of
stochastic differential calculus, previously applied by one of the authors to systems driven by arbitrary delta-correlated processes. In this
context, a straightforward formulation for multi-degree-of-freedom (MDOF) systems is also developed.
Approximate CF solutions to the derived equation are sought for polynomial non-linearities, in stationary conditions. To this aim a wavelet
representation is used, in conjunction with a weighted residual method. Numerical results prove in excellent agreement with exact solutions,
when available, and digital simulation data