First-passage problem for stochastic differential equations with combined parametric Gaussian and Levy white noises via path integral method

We study the first-passage problem for a process governed by a stochastic differential equation (SDE) driven simultaneously by both parametric Gaussian and Levy white noises. We extend the path integral (PI) method to solve the SDE with this combined noise input and the corresponding fractional Fokker-Planck-Kolmogorov equations. Then, the PI solutions are modified to analyze the first-passage problem. Finally, numerical examples based on Monte Carlo simulations verify the extension of the PI method and the modification of the PI solutions. The detailed effects of the system parameters on the first-passage problem are analyzed. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

The study focuses on the first-passage problem of a stochastic differential equation driven by both parametric Gaussian and Levy white noises. The path integral method is extended to solve the equation with combined noise input and the corresponding fractional Fokker-Planck-Kolmogorov equations. Numerical examples validate the method and analyze the effects of system parameters on the first-passage problem.