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  Path integral solutions for n-dimensional stochastic differential equations under α-stable Lévy excitation

Zan, W., Xu, Y., Kurths, J. (2023): Path integral solutions for n-dimensional stochastic differential equations under α-stable Lévy excitation. - Theoretical and Applied Mechanics Letters, 13, 2, 100430.
https://doi.org/10.1016/j.taml.2023.100430

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Zan, Wanrong1, Author
Xu, Yong1, Author
Kurths, Jürgen2, Author              
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1External Organizations, ou_persistent22              
2Potsdam Institute for Climate Impact Research, ou_persistent13              

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 Abstract: In this paper, the path integral solutions for a general n-dimensional stochastic differential equations (SDEs) with -stable Lévy noise are derived and verified. Firstly, the governing equations for the solutions of n-dimensional SDEs under the excitation of -stable Lévy noise are obtained through the characteristic function of stochastic processes. Then, the short-time transition probability density function of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski (CKS) equation and the characteristic function, and its correctness is demonstrated by proving that it satisfies the governing equation of the solution of the SDE, which is also called the Fokker-Planck-Kolmogorov equation. Besides, illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method, and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

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Language(s): eng - English
 Dates: 2023-03-272023-03-07
 Publication Status: Finally published
 Pages: 15
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1016/j.taml.2023.100430
MDB-ID: No data to archive
PIKDOMAIN: RD4 - Complexity Science
Organisational keyword: RD4 - Complexity Science
Research topic keyword: Complex Networks
Research topic keyword: Nonlinear Dynamics
OATYPE: Gold Open Access
 Degree: -

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Title: Theoretical and Applied Mechanics Letters
Source Genre: Journal, Scopus, oa
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Pages: - Volume / Issue: 13 (2) Sequence Number: 100430 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/2095-0349
Publisher: Elsevier