Integrability of stochastic birth-death processes via differential galois theory
Stochastic 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...
- Autores:
-
Acosta-Humánez, Primitivo B.
Capitán, José A.
Morales-Ruiz, Juan J.
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- eng
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/6845
- Palabra clave:
- Diferential Galois theory
Stochastic processes
Population dynamics
Laplace transform
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 Internacional
| Summary: | Stochastic 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. |
|---|