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Responses of
first-order dynamical systems to Matérn, Cauchy, and Dagum
excitations
Lihua Shen, Martin Ostoja-Starzewski and Emilio Porcu
Vol. 3 (2015), No. 1, 27–41
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Abstract |
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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. |
Keywords
random dynamical system, stochastic ordinary differential
equation, fractal, Hurst effect
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Mathematical Subject Classification 2010
Primary: 34F05, 60H10
Secondary: 28A80, 62H10
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Milestones
Received: 15 April 2013
Revised: 14 September 2013
Accepted: 17 November 2013
Published: 13 February 2015
Communicated by Antonio Carcaterra
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Authors |
| Lihua Shen | |
| Department of Computational
Mathematics Capital Normal University Beijing, 100037 China |
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| Martin Ostoja-Starzewski | |
| Department of Mechanical Science and
Engineering University of Illinois at Urbana-Champaign 1206 W. Green Street Urbana, IL 61801-2906 United States |
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| Emilio Porcu | |
| Department of Mathematics University Federico Santa Maria 2360102 Valparaíso Chile |
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