19 citations · 47 across the 11 of their papers we have counts for
12 papers
LAN property for the parameter of the jump rate in mean field interacting systems of neurons
Aline Duarte, Dasha Loukianova, Aurélien Velleret
In the context of a large system of neurons interacting through spike events in a mean-field regime as , we characterize the estimation of a multidimensional param…
Stochastic heterogeneous SIR model with infection-age dependent infectivity on large random graphs
Guodong Pang, Étienne Pardoux, Aurélien Velleret
We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous…
Inter-city infections and the role of size heterogeneity in containment strategies
Viktor Bezborodov, Tyll Krueger, Cornelia Pokalyuk +2
This study examines the effectiveness of regional lockdown strategies in mitigating pathogen spread across regional units, termed cities hereinafter. We develop simplified models t…
Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals
Daehong Kim, Takara Tagawa, Aurélien Velleret
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 o…
Individual based SIS models on (not so) dense large random networks
Jean-François Delmas, Paolo Frasca, Federica Garin +3
Starting from a stochastic individual-based description of an SIS epidemic spreading on a random network, we study the dynamics when the size of the network tends to infinity.…
Metastability between the clicks of Muller's ratchet
Mauro Mariani, Etienne Pardoux, Aurélien Velleret
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…
Large deviations for surviving trajectories of general Markov processes
Aurélien Velleret
The purpose of this paper is to ensure the conditions of Gärtner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the converg…
Individual-based models under various time-scales
Aurélien Velleret
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 demogra…
Adaptation of a population to a changing environment under the light of quasi-stationarity
Aurélien Velleret
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 mo…
Two level natural selection with a quasi-stationarity approach
Aurélien Velleret
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…
Exponential quasi-ergodicity for processes with discontinuous trajectories
Aurélien Velleret
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…
Unique Quasi-Stationary Distribution, with a possibly stabilizing extinction
Aurélien Velleret
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…