Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation
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https://doi.org/10.1007/s00009-019-1338-6 |
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Title
Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential EquationDate
2019-04-16Publisher
Springer Nature Switzerland AGISSN
1660-5446Bibliographic citation
Calatayud, J., Cortés, JC. & Jornet, M. Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential Equation. Mediterr. J. Math. 16, 68 (2019). https://doi.org/10.1007/s00009-019-1338-6Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
In this paper, we deal with uncertainty quantification for the
random Legendre differential equation, with input coefficient A and initial conditions X0 and X1. In a previous study (Calbo et al. in Comput
Math Appl ... [+]
In this paper, we deal with uncertainty quantification for the
random Legendre differential equation, with input coefficient A and initial conditions X0 and X1. In a previous study (Calbo et al. in Comput
Math Appl 61(9):2782–2792, 2011), a mean square convergent power
series solution on (−1/e, 1/e) was constructed, under the assumptions
of mean fourth integrability of X0 and X1, independence, and at most
exponential growth of the absolute moments of A. In this paper, we relax
these conditions to construct an Lp solution (1 ≤ p ≤ ∞) to the random Legendre differential equation on the whole domain (−1, 1), as in
its deterministic counterpart. Our hypotheses assume no independence
and less integrability of X0 and X1. Moreover, the growth condition on
the moments of A is characterized by the boundedness of A, which simplifies the proofs significantly. We also provide approximations of the
expectation and variance of the response process. The numerical experiments show the wide applicability of our findings. A comparison with
Monte Carlo simulations and gPC expansions is performed. [-]
Is part of
Mediterranean Journal of Mathematics, Vol. 16, num. 68 (2019)Funder Name
Ministerio de Economía y Competitividad | Universitat Politècnica de València
Project code
MTM2017-89664-P
Project title or grant
Programa de Ayudas de Investigación y Desarrollo (PAID)
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© Springer Nature Switzerland AG 2019
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