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Simulation of exit times and positions for Brownian motions and Diffusions
Author(s) -
Deaconu Madalina,
Lejay Antoine
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700564
Subject(s) - rectangle , brownian motion , mathematics , position (finance) , monte carlo method , spheres , mathematical analysis , laplace transform , statistical physics , operator (biology) , variance (accounting) , motion (physics) , geometry , physics , classical mechanics , statistics , biochemistry , chemistry , accounting , finance , repressor , business , astronomy , transcription factor , economics , gene
Abstract We present in this note some variations of the Monte Carlo method for the random walk on spheres which allow to solve many elliptic and parabolic problems involving the Laplace operator or second‐order differential operators. In these methods, the spheres are replaced by rectangles or parallelepipeds. Our first method constructs the exit time and the exit position of a rectangle for a Brownian motion. The second method exhibits a variance reduction technique. The main point is to reduce the problem only to the use of some distributions related to the standard one‐dimensional Brownian motion. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)