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Equation governing the probability density evolution of multi-dimensional linear fractional differential systems subject to Gaussian white noise

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Theoretical & Applied Mechanics Letters 2023年第3期13卷 199-208页

作者： Yi Luo Meng-Ze Lyu Jian-Bing Chen Pol D.Spanos George R.Brown School of Engineering Rice UniversityHouston 77005TXUSA Institute for Risk&Reliability Leibniz University HannoverHannover 30167Germany College of Civil Engineering Tongji UniversityShanghai 200092China State Key Laboratory of Disaster Reduction in Civil Engineering Tongji UniversityShanghai 200092China

Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering ***,the determination of their probabilistic responses is difficult due to their non-Markovian *** 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 *** the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is *** 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 *** this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are ***,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 *** examples are studied to assess the merit of the proposed *** 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.

关键词： Globally-evolving-based generalized density evolution equation(GE-GDEE) linear fractional differential system Non-Markovian system Analytical intrinsic drift coefficient Dimension reduction

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