Buongiorno a tutte/i,

ho il piacere di annunciare il prossimo webinar del ciclo di seminari online promosso dal Gruppo UMI PRISMA ( http://www.umi-prisma.polito.it/index.html)

*Lunedi’ 6 febbraio 2023*

*ore 16-17 Antonio Di Crescenzo*

*Titolo: *You can model so many things with birth-death processes

*Abstract:*

Birth-death processes constitute the continuous-time analog of random walks, and are largely adopted as a tool for stochastic modeling. Indeed, the richness of the birth and death rates allows modeling a variety of phenomena, ranging from evolutionary dynamics and neuronal modeling, to queueing and reliability theory, for instance. Various methods of analysis have been developed for determining quantities of interest, such as stationary distributions and first-passage-time distributions.

The talk is aimed at providing a review of some recent results on growth-evolution models characterized by time-dependent growth rates and their stochastic counterpart described by birth-death processes. The analysis focuses on generalizations of the Gompertz and logistic growth models, and on the related birth-death processes having linear and quadratic rates. A diffusion approximation leading to a time-inhomogeneous geometric Brownian motion is also treated. We also present certain generalizations involving extended birth-death processes on a star-graph defined as a lattice formed by the integers of semiaxes joined at the origin. Specifically, we deal with

(i) the analysis of the transient and asymptotic behavior of a multispecies birth-death-immigration process and of a continuous-time multi-type Ehrenfest model,

(ii) the construction and the study of suitable diffusion approximations for the considered models, leading to two processes belonging to the class of Pearson diffusions on the spider.

*ore 17-18* *Daniele Cappelletti*

*Titolo: * Solving the chemical recurrence conjecture in two dimensions

*Abstract:*

Stochastic reaction networks are continuous-time Markov chains typically used in biology, epidemiology, and population dynamics. The goal is to keep track of the abundance of the different reactants over time. What makes them special from a mathematical point of view is the fact that their qualitative dynamics is described by a finite set of allowed transformation rules, referred to as "reaction graph". A long-standing conjecture is that models with a reaction graph composed by a union of strongly connected components are necessarily positive recurrent, meaning that each single state is positive recurrent. In my talk I will discuss why the conjecture makes intuitive sense and why it is difficult to prove it. I will then show how my collaborators and I adapted Forster-Lyapunov techniques to prove the conjecture in two dimensions.

Joint work with: Andrea Agazzi, David Anderson, Jonathan Mattingly

Qui di seguito il link per la partecipazione

https://teams.microsoft.com/l/meetup-join/19%3ad685b25ed15f4821ac5168e63cf98...

Cari saluti,

Claudia Ceci

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Claudia Ceci

Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza (MEMOTEF)

Università di Roma La Sapienza Via Del Castro Laurenziano 9 Roma 00161 Italy

Email: claudia.ceci@uniroma1.it