dc.identifier.uri |
http://dx.doi.org/10.15488/14825 |
|
dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/14944 |
|
dc.contributor.author |
Luo, Yi
|
|
dc.contributor.author |
Lyu, Meng-Ze
|
|
dc.contributor.author |
Chen, Jian-Bing
|
|
dc.contributor.author |
Spanos, Pol D.
|
|
dc.date.accessioned |
2023-09-27T10:10:03Z |
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dc.date.available |
2023-09-27T10:10:03Z |
|
dc.date.issued |
2023 |
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dc.identifier.citation |
Luo, Y.; Lyu, M.-Z.; Chen, J.-B.; Spanos, P.D.: Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise. In: Theoretical and Applied Mechanics Letters (TAML) 13 (2023), Nr. 3, 100436. DOI: https://doi.org/10.1016/j.taml.2023.100436 |
|
dc.description.abstract |
Stochastic fractional differential systems are important and useful in the mathematics, physics, and engineering fields. However, the determination of their probabilistic responses is difficult due to their non-Markovian property. The recently developed globally-evolving-based generalized density evolution equation (GE-GDEE), which is a unified partial differential equation (PDE) governing the transient probability density function (PDF) of a generic path-continuous process, including non-Markovian ones, provides a feasible tool to solve this problem. In the paper, the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established. In particular, it is proved that in the GE-GDEE corresponding to the state-quantities of interest, the intrinsic drift coefficient is a time-varying linear function, and can be analytically determined. In this sense, an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original high-dimensional linear fractional differential system can be constructed such that their transient PDFs are identical. Specifically, for a multi-dimensional linear fractional differential system, if only one or two quantities are of interest, GE-GDEE is only in one or two dimensions, and the surrogate system would be a one- or two-dimensional linear integer-order system. Several examples are studied to assess the merit of the proposed method. Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems, the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian, and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems. |
eng |
dc.language.iso |
eng |
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dc.publisher |
College Park, Md : [Verlag nicht ermittelbar] |
|
dc.relation.ispartofseries |
Theoretical and Applied Mechanics Letters (TAML) 13 (2023), Nr. 3 |
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dc.rights |
CC BY 4.0 Unported |
|
dc.rights.uri |
https://creativecommons.org/licenses/by/4.0 |
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dc.subject |
Analytical intrinsic drift coefficient |
eng |
dc.subject |
Dimension reduction |
eng |
dc.subject |
Globally-evolving-based generalized density evolution equation (GE-GDEE) |
eng |
dc.subject |
Linear fractional differential system |
eng |
dc.subject |
Non-Markovian system |
eng |
dc.subject.ddc |
530 | Physik
|
|
dc.title |
Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise |
eng |
dc.type |
Article |
|
dc.type |
Text |
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dc.relation.essn |
2095-0349 |
|
dc.relation.doi |
https://doi.org/10.1016/j.taml.2023.100436 |
|
dc.bibliographicCitation.issue |
3 |
|
dc.bibliographicCitation.volume |
13 |
|
dc.bibliographicCitation.firstPage |
100436 |
|
dc.description.version |
publishedVersion |
|
tib.accessRights |
frei zug�nglich |
|