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math.PR2025
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…
math.PR2024
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…
math.PR2020
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…