IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v10y2008i4d10.1007_s11009-008-9070-x.html
   My bibliography  Save this article

First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes

Author

Listed:
  • Andrew N. Downes

    (University of Melbourne)

  • Konstantin Borovkov

    (University of Melbourne)

Abstract

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one. In doing so we establish the existence of the first-passage time density and provide an upper bound for this function. In the case of processes with diffusion interval equal to ℝ this is extended to a lower bound, as well as bounds for the first crossing time of a lower boundary. An extension to some time-inhomogeneous diffusions is given. These results are illustrated by numerical examples.

Suggested Citation

  • Andrew N. Downes & Konstantin Borovkov, 2008. "First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 621-644, December.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:4:d:10.1007_s11009-008-9070-x
    DOI: 10.1007/s11009-008-9070-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-008-9070-x
    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/s11009-008-9070-x?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. Liqun Wang & Klaus Pötzelberger, 2007. "Crossing Probabilities for Diffusion Processes with Piecewise Continuous Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 21-40, March.
    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. Borovkov, K. & Downes, A.N., 2010. "On boundary crossing probabilities for diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 105-129, February.
    2. Downes, A.N., 2009. "Bounds for the transition density of time-homogeneous diffusion processes," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 835-841, March.

    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. Mario Abundo, 2010. "On the First Hitting Time of a One-dimensional Diffusion and a Compound Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 473-490, September.
    2. Qinglai Dong & Lirong Cui, 2019. "First Hitting Time Distributions for Brownian Motion and Regions with Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 1-23, March.
    3. Hangsuck Lee & Hongjun Ha & Minha Lee, 2022. "Piecewise linear boundary crossing probabilities, barrier options, and variable annuities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2248-2272, December.
    4. Lee, Taeho, 2023. "Exact simulation for the first hitting time of Brownian motion and Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 193(C).
    5. Zhiyong Jin & Liqun Wang, 2017. "First Passage Time for Brownian Motion and Piecewise Linear Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 237-253, March.
    6. Hangsuck Lee & Hongjun Ha & Minha Lee, 2022. "Piecewise linear double barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(1), pages 125-151, January.

    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:10:y:2008:i:4:d:10.1007_s11009-008-9070-x. 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.