Research reports

Years: 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Computing exit times with the Euler scheme

by F. M. Buchmann

(Report number 2003-02)

Abstract
In this note we study standard Euler updates for computing first exit times of general diffusions from a domain. We focus on one dimensional situations and show how the ideas of Mannella and Gobet can be adapted to this problem. In particular, we give a fully implementable algorithm to compute the first exit time from an interval numerically. The Brownian motion case is treaten in detail. Special emphasize is on numerical experiments: For every ansatz, we include numerical experiments confirming the conjectured accuracy of our methods. Our methods appear to be at least of weak order one and give improved results at the same computational cost compared to algorithms used widely in practice.

Keywords:

@Techreport{B03_314,
  author = {F. M. Buchmann},
  title = {Computing exit times with the Euler scheme},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-02.pdf },
  year = {2003}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).