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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Títol
Improving the Approximation of the First- and Second-Order Statistics of the Response Stochastic Process to the Random Legendre Differential EquationData de publicació
2019-04-16Editor
Springer Nature Switzerland AGISSN
1660-5446Cita bibliogràfica
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/s00009-019-1338-6Tipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
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. [-]
Publicat a
Mediterranean Journal of Mathematics, Vol. 16, num. 68 (2019)Entitat finançadora
Ministerio de Economía y Competitividad | Universitat Politècnica de València
Codi del projecte o subvenció
MTM2017-89664-P
Títol del projecte o subvenció
Programa de Ayudas de Investigación y Desarrollo (PAID)
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© Springer Nature Switzerland AG 2019
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