14 citations · 39 across the 11 of their papers we have counts for
13 papers
Brownian particles controlled by their occupation measure
Loïc Béthencourt, Rémi Catellier, Etienne Tanré
In this article, we study a finite horizon linear-quadratic stochastic control problem for Brownian particles, where the cost functions depend on the state and the occupation measu…
On the Robustness of Text Vectorizers
Rémi Catellier, Samuel Vaiter, Damien Garreau
A fundamental issue in machine learning is the robustness of the model with respect to changes in the input. In natural language processing, models typically contain a first embedd…
Regularization by noise for rough differential equations driven by Gaussian rough paths
Rémi Catellier, Romain Duboscq
We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely non-determinism, and uniform el…
Pathwise regularization of the stochastic heat equation with multiplicative noise through irregular perturbation
Rémi Catellier, Fabian A. Harang
Existence and uniqueness of solutions to the stochastic heat equation with multiplicative spatial noise is studied. In the spirit of pathwise regularization by noise, we show that…
A mean-field approach to self-interacting network, convergence and regularity
Rémi Catellier, Yves D'Angelo, Cristiano Ricci
The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a networ…
Propagation of chaos for mean field rough differential equations
I. Bailleul, R. Catellier, F. Delarue
We address propagation of chaos for large systems of rough differential equations associated with random rough differential equations of mean field type $$ dX_t = V(X_t,\mathcal{L}…
Non-explosion criteria for rough differential equations driven by unbounded vector fields
I. Bailleul, R. Catellier
We give in this note a simple treatment of the non-explosion problem for rough differential equations driven by unbounded vector fields and weak geometric rough paths of arbitrary…
Solving mean field rough differential equations
I. Bailleul, R. Catellier, F. Delarue
We provide in this work a robust solution theory for random rough differential equations of mean field type wh…
Average-case complexity of a branch-and-bound algorithm for maximum independent set, under the random model
N. Bourgeois, R. Catellier, T. Denat +1
We study average-case complexity of branch-and-bound for maximum independent set in random graphs under the distribution. In this model every pair of ver…
Rough linear transport equation with an irregular drift
Rémi Catellier
We study the linear transport equation \[ \frac{\partial}{\partial t} u ( t,x ) +b ( t,x ) \cdot \nabla u ( t,x ) + \nabla u ( t,x ) \cdot \frac{\partial}{\partial t} X ( t ) =0, \…
Paracontrolled Distributions and the 3-dimensional Stochastic Quantization Equation
Rémi Catellier, Khalil Chouk
We prove the existence and uniqueness of a local solution to the periodic renormalized model of stochastic quantisation using the method of controlled distributions introdu…
Averaging along irregular curves and regularisation of ODEs
R. Catellier, M. Gubinelli
We consider the ordinary differential equation (ODE) where is a continuous driving function and is a time-dependent vector field which poss…
The emergence of French statistics. How mathematics entered the world of statistics in France during the 1920s
Rémi Catellier, Laurent Mazliak
This paper concerns the emergence of modern mathematical statistics in France after the First World War. Emile Borel's achievements are presented, and especially his creation of tw…