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math.PR2026
LU-type factorizations and Darboux transformations for continuous-time birth--death processes
José Arcia-Manoleskos, Manuel Domínguez de la Iglesia
We study LU-type factorizations of the infinitesimal generator of a possibly nonconservative birth--death process on , and characterize those for which the correspond…
math.PR2021
An urn model for the Jacobi-Piñeiro polynomials
F. Alberto Grünbaum, Manuel D. de la Iglesia
The list of physically motivated urn models that can be solved in terms of classical orthogonal polynomials is very small. It includes a model proposed by D. Bernoulli and further…
math.PR2020
Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformations
Manuel D. de la Iglesia, Claudia Juarez
We consider a new way of factorizing the transition probability matrix of a discrete-time birth-death chain on the integers by means of an absorbing and a reflecting birth-death ch…