8 papers
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…
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…
High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods
Eugen Bronasco, Adrien Busnot Laurent, Baptiste Huguet
We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In o…
Logarithmic Sobolev inequalities for generalised Cauchy measures
Baptiste Nicolas Huguet
We prove a curvature-dimension criterion and obtain logarithmic Sobolev inequalities for generalised Cauchy measures with optimal weights and explicit constants. In the one-dimensi…
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…
Poincar{é} inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures
Baptiste Nicolas Huguet
We obtain new sharp weighted Poincar{é} inequalities on Riemannian manifolds for a general class of measures. When specialised to generalised Cauchy measures, this gives a unified…
Brenier-Schr{ö}dinger problem on compact manifold with boundary
David García-Zelada, Baptiste Huguet
We consider the Brenier-Schr{ö}dinger problem on compact manifolds with boundary. In the spirit of a work by Arnaudon, Cruzeiro, L{é}onard and Zambrini, we study the kinetic proper…
Intertwining relations for diffusions in manifolds and applications to functional inequalities
Baptiste Huguet
We prove intertwining relations by twisted gradients for Markov semi-groups. These relations are applied to Brascamp-Lieb type inequalities and spectral gap results. It generalizes…