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Open AccessArticle

Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points

1
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
2
Department of Statistics and Operational Research, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(2), 230; https://doi.org/10.3390/math8020230
Received: 17 January 2020 / Revised: 4 February 2020 / Accepted: 5 February 2020 / Published: 10 February 2020
In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation. View Full-Text
Keywords: random variable transformation technique; second-order random linear differential equation; regular-singular point; first probability density function random variable transformation technique; second-order random linear differential equation; regular-singular point; first probability density function
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Cortés, J.-C.; Navarro-Quiles, A.; Romero, J.-V.; Roselló, M.-D. Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points. Mathematics 2020, 8, 230.

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