Showing papers by "Antoine Lejay published in 2002"
TL;DR: In this article, the weak solution of a semi-linear system of parabolic PDEs with a second-order divergence-form partial differential operator and possibly discontinuous coefficients is proved by approximation.
26 citations
TL;DR: The double porosity model allows one to compute the pressure at a macroscopic scale in a fractured porous media, but requires the computation of some exchange coefficient characterizing the passage of the fluid from and to the porous media (the matrix and the fractures).
Abstract: The double porosity model allows one to compute the pressure at a macroscopic scale in a fractured porous media, but requires the computation of some exchange coefficient characterizing the passage of the fluid from and to the porous media (the matrix) and the fractures This coefficient may be numerically computed by some Monte Carlo method, by evaluating the time a Brownian particle spends in the matrix and the fissures Although we simulate some stochastic processes, the approach presented here does not use approximation by random walks, and then does not require any discretization We are interested only in the particles in the matrix A first approximation of the exchange coefficient may then be computed In a forthcoming paper, we will present the simulation of the particles in the fissures
16 citations
Journal Article•
TL;DR: In this paper, the decomposition of the excursions measure as convex combination of excursions measures of reflected processes is computed in order to characterize the discontinuity at one point of the diffusion coefficient.
Abstract: The coefficients in the decomposition of the excursions measure as convex combination of excursions measures of reflected processes are computed in order to characterize the discontinuity at one point of the diffusion coefficient. In some sense, this result extends to general diffusions a similar one for the skew Brownian motion, and we advocate it may be used in Monte Carlo methods for discontinuous media.
15 citations
TL;DR: In this article, the limit of functionals of stochastic processes for which an homogenization result holds was studied and counterexamples to the theory of good sequence of semimartingales were provided.
Abstract: We study the limit of functionals of stochastic processes for which an homogenization result holds. All these functionals involve stochastic integrals. Among them, we consider more particularly the Levy area and those giving the solutions of some SDEs. The main question is to know whether or not the limit of the stochastic integrals is equal to the stochastic integral of the limit of each of its terms. In fact, the answer may be negative, especially in presence of a highly oscillating first-order differential term. This provides us some counterexamples to the theory of good sequence of semimartingales.
12 citations
01 Jan 2002
TL;DR: The double porosity model allows to compute the pres- sure at a macroscopic scale in a fractured porous media, but re- quires the computation of some exchange coefficient characteriz- ing the passage of the fluid from and to the porous media (the matrix) and the fractures.
Abstract: The double porosity model allows to compute the pres- sure at a macroscopic scale in a fractured porous media, but re- quires the computation of some exchange coefficient characteriz- ing the passage of the fluid from and to the porous media (the matrix) and the fractures. This coefficient may be numerically computed by some Monte-Carlo method, by evaluating the aver- age time a Brownian particle spend in the matrix and the fissures. Although we simulate some stochastic process, the approach pre- sented here does not use approximation by random walks, and then does not require any discretization.
2 citations