6533b82bfe1ef96bd128ce2a
RESEARCH PRODUCT
Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments
Gioacchino AlottaM. Di Paolasubject
Statistics and ProbabilityFractional Fokker-Planck equationα-stable white noiseMathematical analysisProbabilistic logicStatistical and Nonlinear PhysicsProbability density functionCondensed Matter PhysicWhite noiseComplex fractional momentStability (probability)Fractional calculusMechanical systemNonlinear systemNonlinear systemRange (statistics)Complex fractional moments; Fractional Fokker-Planck equation; Nonlinear systems; α-stable white noise; Condensed Matter Physics; Statistics and ProbabilityMathematicsdescription
Abstract The probability density function of the response of a nonlinear system under external α -stable Levy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Levy white noise with different stability indexes α . Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Levy white noise.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-02-01 | Physica A: Statistical Mechanics and its Applications |