Masterclass MINT 07/05/2026

jeudi 7 mai 2026, 12:15 → 13:15 Europe/Paris

Salle F. Pellos (1R2-207) (Institut de Mathématiques de Toulouse (IMT))

Intervenant :     Josué Tchouanti Fotso (IMT)

Title : An introduction to birth-death processes

Abstract: This presentation provides an introduction to birth and death processes, a fundamental class of continuous-time Markov chains that arise in many areas of applied probability. These processes model the evolution of a discrete system whose state changes through elementary transitions corresponding to "births" and "deaths", and they offer a particularly tractable framework for studying stochastic dynamics.
After introducing the formal setting and some key properties (transition rates, infinitesimal generator and Markov structure), we will present several classical examples drawn from queueing theory and population dynamics. We will then examine the associated Kolmogorov equations, as well as the conditions for the existence and the explicit form of stationary distributions.
Finally, we will discuss the long-term behavior of these processes and briefly mention some extensions and contemporary applications. This presentation aims to provide both a solid theoretical understanding and practical tools for analyzing stochastic models.