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

Wanrong Zan; Yong Xu; Ralf Metzler; Jürgen Kurths

doi:10.1016/j.jcp.2021.110264

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

Wanrong Zan, Yong Xu, Ralf Metzler, Jürgen Kurths

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

We study the first-passage problem for a process governed by a stochastic differential equation (SDE) driven simultaneously by both parametric Gaussian and Lévy 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.

Original language	English
Article number	110264
Journal	Journal of Computational Physics
Volume	435
DOIs	https://doi.org/10.1016/j.jcp.2021.110264
State	Published - 15 Jun 2021

Keywords

Combined parametric Gaussian and Lévy white noises
First-passage problem
Fractional Fokker-Planck-Kolmogorov equation
Monte Carlo simulation
Path integral method
Stochastic differential equation

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10.1016/j.jcp.2021.110264

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title = "First-passage problem for stochastic differential equations with combined parametric Gaussian and L{\'e}vy white noises via path integral method",

abstract = "We study the first-passage problem for a process governed by a stochastic differential equation (SDE) driven simultaneously by both parametric Gaussian and L{\'e}vy 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.",

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AU - Zan, Wanrong

AU - Xu, Yong

AU - Metzler, Ralf

AU - Kurths, Jürgen

PY - 2021/6/15

Y1 - 2021/6/15

N2 - We study the first-passage problem for a process governed by a stochastic differential equation (SDE) driven simultaneously by both parametric Gaussian and Lévy 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.

AB - We study the first-passage problem for a process governed by a stochastic differential equation (SDE) driven simultaneously by both parametric Gaussian and Lévy 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.

KW - Combined parametric Gaussian and Lévy white noises

KW - First-passage problem

KW - Fractional Fokker-Planck-Kolmogorov equation

KW - Monte Carlo simulation

KW - Path integral method

KW - Stochastic differential equation

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DO - 10.1016/j.jcp.2021.110264

M3 - 文章

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SN - 0021-9991

VL - 435

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 110264

ER -

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

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