exitbm

The exitbm library provides methods to simulate random variables related to the first exit time and position of the Brownian motion from simple domains, namely intervals, squares and rectangles.

This library may be used in order to implements Monte Carlo methods such as the random walk on squares and on rectangles, which are variant to the random walk on spheres with the advantage of having explicitly and exactly the exit time. These algorithms allow one to solve the Dirichlet problem, but also other linear problems as well as computing the first eigenvalue of the Laplace operator or other quantities related to this operator.

It is written in standard C and relies on the GNU scientific library (GSL). It provides: - Density and distribution and realizations of the first exit time from an interval for the Brownian motion, given the exit point is one of the endpoint or not known. - Density, distribution function and realizations of the position of the Brownian motion at a given time, given the exit time is known or known to be greater than a given value. - Realizations of the first exit time and position from an interval. - Realizations of the first exit time and position from a centered interval for a Skew Brownian motion. - Realizations of the first exit time and position from a square centered on the position of the Brownian motion. - Realizations of the first exit time and position from a rectangle.

Download

This library and its documentation may be downloaded from the Gforge project exitbm at INRIA. It us provided under the free software CeCILL licence.

Version 2.3 is out ! (April 2012)

This version includes the source code of the numerical tests of the article A. Lejay, S. Maire, New Monte Carlo schemes for simulating diffusions in discontinuous media (2012).

Author

This library has been developped by Antoine Lejay (project-team TOSCA, INRIA Nancy Grand-Est, IECN) and is inspired by the works of G.N. Milstein & M.V. Tretyakov, O. Faure and his own collaborations with Fabien Campillo, Madalina Deaconu, Sylvain Maire, Miguel Martinez and Samih Zein.

Last update of this document: 23 April 2012