IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v8y2006i1d10.1007_s11009-006-7292-3.html
   My bibliography  Save this article

A Random Walk on Rectangles Algorithm

Author

Listed:
  • Madalina Deaconu

    (INRIA Lorraine and Institut Élie Cartan de Nancy (IECN))

  • Antoine Lejay

    (INRIA Lorraine and Institut Élie Cartan de Nancy (IECN))

Abstract

In this article, we introduce an algorithm that simulates efficiently the first exit time and position from a rectangle (or a parallelepiped) for a Brownian motion that starts at any point inside. This method provides an exact way to simulate the first exit time and position from any polygonal domain and then to solve some Dirichlet problems, whatever the dimension. This method can be used as a replacement or complement of the method of the random walk on spheres and can be easily adapted to deal with Neumann boundary conditions or Brownian motion with a constant drift.

Suggested Citation

  • Madalina Deaconu & Antoine Lejay, 2006. "A Random Walk on Rectangles Algorithm," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 135-151, March.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:1:d:10.1007_s11009-006-7292-3
    DOI: 10.1007/s11009-006-7292-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-006-7292-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-006-7292-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sabelfeld K.K. & Talay D., 1995. "Integral Formulation of the Boundary Value Problems and the Method of Random Walk on Spheres," Monte Carlo Methods and Applications, De Gruyter, vol. 1(1), pages 1-34, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Deaconu, M. & Herrmann, S. & Maire, S., 2017. "The walk on moving spheres: A new tool for simulating Brownian motion’s exit time from a domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 28-38.
    2. Maire, Sylvain & Nguyen, Giang, 2016. "Stochastic finite differences for elliptic diffusion equations in stratified domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 146-165.
    3. Lejay, Antoine & Maire, Sylvain, 2007. "Computing the principal eigenvalue of the Laplace operator by a stochastic method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 351-363.
    4. Gobet, Emmanuel & Menozzi, Stéphane, 2010. "Stopped diffusion processes: Boundary corrections and overshoot," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 130-162, February.
    5. Karl K. Sabelfeld & Anastasia E. Kireeva, 2022. "Stochastic Simulation Algorithms for Solving Transient Anisotropic Diffusion-recombination Equations and Application to Cathodoluminescence Imaging," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3029-3048, December.
    6. Sabelfeld, Karl K. & Kireeva, Anastasya, 2020. "Stochastic simulation algorithms for solving a nonlinear system of drift–diffusion-Poisson equations of semiconductors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    7. Bras, Pierre & Kohatsu-Higa, Arturo, 2023. "Simulation of reflected Brownian motion on two dimensional wedges," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 349-378.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sabelfeld Karl K. & Shalimova Irina A., 2002. "Random Walk on Spheres methods for iterative solution of elasticity problems," Monte Carlo Methods and Applications, De Gruyter, vol. 8(2), pages 171-202, December.
    2. Sabelfeld K.K. & Shalimova I.A., 1995. "Random Walk on Spheres Process for Exterior Dirichlet Problem," Monte Carlo Methods and Applications, De Gruyter, vol. 1(4), pages 325-331, December.
    3. Deaconu, M. & Herrmann, S. & Maire, S., 2017. "The walk on moving spheres: A new tool for simulating Brownian motion’s exit time from a domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 28-38.
    4. Shalimova, I.A., 1998. "A Monte Carlo iterative procedure for solving the pseudo-vibration elastic equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 449-453.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:8:y:2006:i:1:d:10.1007_s11009-006-7292-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.