Showing papers by "Antoine Lejay published in 2011"
TL;DR: In this paper, the authors provide a simulation algorithm for a diffusion process in a layered media using the Skew Brownian motion and a path decomposition technique for simulating occupation times.
Abstract: In this note, we provide a simulation algorithm for a diffusion process in a layered media. Our main tools are the properties of the Skew Brownian motion and a path decomposition technique for simulating occupation times.
20 citations
01 Jan 2011
TL;DR: The Seminaire de Probabilites as mentioned in this paper contains about 20 original research and survey articles on topics related to stochastic analysis, including the representation formulae for fractional Brownian motion.
Abstract: This is a new volume of the Seminaire de Probabilites which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journees de Probabilites held in Poitiers in June 2009.
13 citations
14 Oct 2011
TL;DR: In this paper, weak approximations of multi-dimensional stochastic differential equations with discontinuous drift coefficients are considered and a rate of weak convergence of the Euler-Maruyama approximation of SDEs with approximated drift coefficients is provided.
Abstract: In this paper, weak approximations of multi-dimensional stochastic differential equations with discontinuous drift coefficients are considered. Here as the approximated process, the Euler-Maruyama approximation of SDEs with approximated drift coefficients is used, and we provide a rate of weak convergence of them. Finally we present a rate of weak convergence of the Euler-Maruyama approximation of the original SDEs with constant diffusion coefficients.
10 citations
01 Feb 2011
TL;DR: The C library as discussed by the authors aims at computing and simulating various quantities and random variables related to where and when a Brownian motion hit the boundary of an interval, a square or a rectangle.
Abstract: This C library aims at computing and simulating various quantities and random variables related to where and when a the Brownian motion hit the boundary of an interval, a square or a rectangle. We present here the algorithms used in this library.
6 citations
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TL;DR: In this article, the authors 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 discretization.
Abstract: 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 discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the Skew Brownian motion being an usual Brownian motion. This allows to design a test on the skewness parameter. We show that numerical simulations that can be easily performed to estimate the skewness parameter, and provide an application in Biology.