6533b82dfe1ef96bd1290b1a
RESEARCH PRODUCT
Path Integral Method for Nonlinear Systems Under Levy White Noise
Antonina PirrottaAntonina PirrottaAlberto Di Matteosubject
Mechanical EngineeringMathematical analysisShot noise020101 civil engineering02 engineering and technologyWhite noiseLevy white noiseStability (probability)Stochastic Response0201 civil engineeringPath Integral SolutionNonlinear systemsymbols.namesake020303 mechanical engineering & transportsAdditive white Gaussian noise0203 mechanical engineeringGaussian noisePath integral formulationsymbolsSafety Risk Reliability and QualitySafety ResearchMathematicsdescription
In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The path integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, the path integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein–Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under different values of alpha is reported. Comparisons with pertinent Monte Carlo simulation data and analytical solutions (when available) demonstrate the accuracy of the results.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-06-12 |