Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 435, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2021.110264
Keywords
First-passage problem; Stochastic differential equation; Fractional Fokker-Planck-Kolmogorov equation; Path integral method; Monte Carlo simulation; Combined parametric Gaussian and Levy white noises
Funding
- National Natural Science Foundation of China [11772255, 12072264]
- Fundamental Research Funds for the Central Universities
- Research Funds for Interdisciplinary Subject of Northwestern Polytechnical University
- Shaanxi Project for Distinguished Young Scholars, Shaanxi Provincial Key RD Program [2020KW-013, 2019TD-010]
- National Key Research and Development Program of China [2018AAA0102201]
- Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University [CX202045]
- German Research Foundation (DFG) [ME 1535/7-1]
- Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej, FNP) within an Alexander von Humboldt Honorary Polish Research Scholarship
- project RF Government [0751520191885]
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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.
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.
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