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Lookup NU author(s): Professor Emilio Porcu
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The responses of dynamical systems under random forcings is a well-understood area of research. The main tool in this area, as it has evolved over a century, falls under the heading of stochastic differential equations. Most works in the literature are related to random forcings with a known parametric spectral density. This paper considers a new framework: the Cauchy and Dagum covariance functions indexing the random forcings do not have a closed form for the associated spectral density, while allowing decoupling of the fractal dimension and Hurst effect. On the basis of a first-order stochastic differential equation, we calculate the transient second-order characteristics of the response under these two covariances and make comparisons to responses under white, Ornstein–Uhlenbeck, and Matérn noises.
Author(s): Shen L, Ostoja-Starzewski M, Porcu E
Publication type: Article
Publication status: Published
Journal: Mathematics and Mechanics of Complex Systems
Year: 2015
Volume: 3
Issue: 1
Pages: 27–41
Print publication date: 13/02/2015
Acceptance date: 17/11/2013
ISSN (print): 2326-7186
ISSN (electronic): 2325-3444
Publisher: International Research Center for the Mathematics and Mechanics of Complex Systems
URL: https://doi.org/10.2140/memocs.2015.3.27
DOI: 10.2140/memocs.2015.3.27
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