Acosta-Humánez, Primitivo B.Capitán, José A.Morales-Ruiz, Juan J.2020-12-042020-12-04202017606101https://hdl.handle.net/20.500.12442/6845Stochastic birth-death processes are described as continuous-time Markov processes in models of population dynamics. A system of in nite, coupled ordinary diferential equations (the so- called master equation) describes the time-dependence of the probability of each system state. Using a generating function, the master equation can be transformed into a partial diferential equation. In this contribution we analyze the integrability of two types of stochastic birth-death processes (with polynomial birth and death rates) using standard diferential Galois theory.We discuss the integrability of the PDE via a Laplace transform acting over the temporal variable. We show that the PDE is not integrable except for the case in which rates are linear functions of the number of individuals.pdfengAttribution-NonCommercial-NoDerivatives 4.0 InternacionalDiferential Galois theoryStochastic processesPopulation dynamicsLaplace transforminfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://doi.org/10.1051/mmnp/2020005