179 citations · 335 across the 13 of their papers we have counts for
14 papers · 1 filter
General diffusion processes as the limit of time-space Markov chains
Alexis Anagnostakis, Antoine Lejay, Denis Villemonais
We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes w…
The non-linear sewing lemma III: Stability and generic properties
Antoine Brault, Antoine Lejay
Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discre…
The non-linear sewing lemma II: Lipschitz continuous formulation
Antoine Brault, Antoine Lejay
We give an unified framework to solve rough differential equations. Based on flows, our approach unifies the former ones developed by Davie, Friz-Victoir and Bailleul. The main ide…
The non-linear sewing lemma I : weak formulation
Antoine Brault, Antoine Lejay
We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak c…
Maximum likelihood drift estimation for a threshold diffusion
Antoine Lejay, Paolo Pigato
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and neg…
Sensitivity of rough differential equations: an approach through the Omega lemma
Laure Coutin, Antoine Lejay
The It{ô} map assigns the solution of a Rough Differential Equation, a generalization of an Ordinary Differential Equation driven by an irregular path, when existence and uniquenes…
Statistical estimation of the Oscillating Brownian Motion
Antoine Lejay, Paolo Pigato
We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Us…
The snapping out Brownian motion
Antoine Lejay
We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at with a jump proportional to its flux. This kind of interfa…
Is a Brownian skew?
Antoine Lejay, Ernesto Mordecki, Soledad Torres
We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretizati…
Simulation of diffusions by means of importance sampling paradigm
Madalina Deaconu, Antoine Lejay
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to…
Global existence for rough differential equations under linear growth conditions
Massimiliano Gubinelli, Antoine Lejay
We prove existence of global solutions for differential equations driven by a geometric rough path under the condition that the vector fields have linear growth. We show by an expl…
On the constructions of the skew Brownian motion
Antoine Lejay
This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numeri…
A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients
Antoine Lejay, Miguel Martinez
The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coeffi…
Young integrals and SPDEs
Antoine Lejay, Massimiliano Gubinelli, Samy Tindel
In this note, we study the non-linear evolution problem , where is a -Hölder continuous function of the time parameter, with values in a dist…