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

Author

Listed:
  • Juan-Carlos Cortés

    (Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
    These authors contributed equally to this work.)

  • Ana Navarro-Quiles

    (Department of Statistics and Operational Research, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Spain
    These authors contributed equally to this work.)

  • José-Vicente Romero

    (Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
    These authors contributed equally to this work.)

  • María-Dolores Roselló

    (Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Juan-Carlos Cortés & Ana Navarro-Quiles & José-Vicente Romero & María-Dolores Roselló, 2020. "Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points," Mathematics, MDPI, vol. 8(2), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:230-:d:318891
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    References listed on IDEAS

    as
    1. Cortés, J.-C. & Navarro-Quiles, A. & Romero, J.-V. & Roselló, M.-D., 2018. "Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 33-45.
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