First-passage problem for nonlinear systems under Lévy white noise through path integral method

Abstract

In this paper, the first-passage problem for nonlinear systems driven by (Formula presented.)-stable Lévy white noises is considered. The path integral solution (PIS) is adopted for determining the reliability function and first-passage time probability density function of nonlinear oscillators. Specifically, based on the properties of (Formula presented.)-stable random variables and processes, PIS is extended to deal with Lévy white noises with any value of the stability index (Formula presented.). Application to linear and nonlinear systems considering different values of (Formula presented.) is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.