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

Juan-Carlos Cortés, Ana Navarro-Quiles, José-Vicente Romero and María-Dolores Roselló
Additional contact information
Juan-Carlos Cortés: Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Ana Navarro-Quiles: Department of Statistics and Operational Research, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Spain
José-Vicente Romero: Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
María-Dolores Roselló: Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Mathematics, 2020, vol. 8, issue 2, 1-19

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.

Keywords: random variable transformation technique; second-order random linear differential equation; regular-singular point; first probability density function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/230/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/230/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:2:p:230-:d:318891

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().