Path Integral Method for Nonlinear Systems Under Levy White Noise

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Abstract

In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Levy 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 Levy 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
Lingua originaleEnglish
pagine (da-a)030905-
Numero di pagine7
RivistaASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS. PART B. MECHANICAL ENGINEERING
Volume3
Stato di pubblicazionePublished - 2017

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All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Safety, Risk, Reliability and Quality
  • Safety Research

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