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math.PR2026
Law of large numbers for stochastic multiscale spatial gene networks
Arnaud Debussche, Baptiste Huguet
We study a stochastic multiscale spatial gene network. These naturally arise in molecular biology. In our model, the reactants are subject to on-site reactions on both scales and d…
math.PR2025
Strong approximation and central limit theorems for multiscale stochastic gene networks
Baptiste Nicolas Huguet
We study a mutliscale jump process introduced in a work by Crudu, Debussche, Muller and Radulescu. Using an adequate coupling, we are able to prove the strong convergence, for the…
math.PR2024
The Brenier-Schrödinger problem with respect to Feller semimartingales and non-local Hamilton-Jacobi-Bellman equations
Ronan Herry, Baptiste Huguet
Motivated by a problem from incompressible fluid mechanics of Brenier (JAMS 1989), and its recent entropic relaxation by Arnaudo, Cruizero, Léonard & Zambrini (AIHP PS 2020), we st…