First-passage problem for nonlinear systems under L,vy white noise through path integral method

In this paper, the first-passage problem for nonlinear systems driven by -stable L,vy 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 -stable random variables and processes, PIS is extended to deal with L,vy white noises with any value of the stability index . Application to linear and nonlinear systems considering different values of is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.