6533b86efe1ef96bd12cb5e1
RESEARCH PRODUCT
Stochastic response of linear and non-linear systems to α-stable Lévy white noises
Giuseppe FaillaMario Di Paolasubject
Non-Gaussian inputDifferential equationMechanical EngineeringCharacteristic equationAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsDifferential calculusWhite noiseCondensed Matter PhysicsMethod of mean weighted residualsNonlinear systemStochastic differential equationExact solutions in general relativityNuclear Energy and EngineeringCalculusApplied mathematicsα-stable Lévy white noiseStochastic differential calculusCivil and Structural EngineeringMathematicsdescription
Abstract The stochastic response of linear and non-linear systems to external α -stable Levy 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-04-01 |