Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Velleret, Aurélien"'
We study the effectiveness of regional lockdown strategies to mitigate the spread of a pathogen across regional units, in the following called cities, within a country or region for a single infection wave. The heterogeneity in the epidemically relev
Externí odkaz:
http://arxiv.org/abs/2402.03100
We study the long-time behavior of an additive functional that takes into account the jumps of a symmetric Markov process. This process is assumed to be observed through a biased observation scheme that includes the survival to events of extinction a
Externí odkaz:
http://arxiv.org/abs/2401.17997
Autor:
Delmas, Jean-François, Frasca, Paolo, Garin, Federica, Tran, Viet Chi, Velleret, Aurélien, Zitt, Pierre-André
Publikováno v:
ALEA, Lat. Am. J. Probab. Math. Stat. 21, 1375-1405 (2024)
Starting from a stochastic individual-based description of an SIS epidemic spreading on a random network, we study the dynamics when the size $n$ of the network tends to infinity. We recover in the limit an infinite-dimensional integro-differential e
Externí odkaz:
http://arxiv.org/abs/2302.13385
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual reproduction mode in
Externí odkaz:
http://arxiv.org/abs/2007.14715
Autor:
Velleret, Aurélien
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied efficiently.
Externí odkaz:
http://arxiv.org/abs/2003.01026
Autor:
Velleret, Aurélien
Publikováno v:
ESAIM: PROCEEDINGS AND SURVEYS 68 (2020) 123-152
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the individua
Externí odkaz:
http://arxiv.org/abs/1912.00921
Autor:
Velleret, Aurélien
Publikováno v:
Discrete and Continuous Dynamical Systems - B, 2023
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups. We then ob
Externí odkaz:
http://arxiv.org/abs/1903.10161
Autor:
Velleret, Aurélien
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion modeling p
Externí odkaz:
http://arxiv.org/abs/1903.10165
Autor:
Velleret, Aurélien
This paper tackles the issue of establishing a lower-bound on the asymptotic ratio of survival probabilities between two different initial conditions, asymptotically in time for a given Markov process with extinction. Such a comparison is a crucial s
Externí odkaz:
http://arxiv.org/abs/1902.01441
Autor:
Velleret, Aurélien
Publikováno v:
Stochastic Processes and their Applications 148 (2022) 98-138
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process conditionned upo
Externí odkaz:
http://arxiv.org/abs/1802.02409