IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v205y2024ics0167715223001803.html
   My bibliography  Save this article

Exact solution to a first-passage problem for an Ornstein–Uhlenbeck process with jumps and its integral

Author

Listed:
  • Lefebvre, Mario

Abstract

Let dX(t)=Y(t)dt, where Y(t) is an Ornstein–Uhlenbeck process with Poissonian jumps, and let T(x,y) be the first time that X(t)+Y(t)=0, given that X(0)=x and Y(0)=y. The moment-generating function of T(x,y) is obtained in the case when the jumps are exponentially distributed by solving the integro-differential equation it satisfies, subject to the appropriate boundary conditions. The case when the jumps are uniformly distributed is also considered.

Suggested Citation

  • Lefebvre, Mario, 2024. "Exact solution to a first-passage problem for an Ornstein–Uhlenbeck process with jumps and its integral," Statistics & Probability Letters, Elsevier, vol. 205(C).
    • Handle: RePEc:eee:stapro:v:205:y:2024:i:c:s0167715223001803
    DOI: 10.1016/j.spl.2023.109956
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715223001803
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109956?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. Abundo, Mario & Pirozzi, Enrica, 2018. "Integrated stationary Ornstein–Uhlenbeck process, and double integral processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 265-275.
    2. Makasu, Cloud, 2009. "Exit probability for an integrated geometric Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1363-1365, June.
    3. Lefebvre, Mario, 1989. "Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 281-287, August.
    Full references (including those not matched with items on IDEAS)

    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 Lefebvre, 2003. "First-passage problems for degenerate two-dimensional diffusion processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 125-139, June.
    2. Mario Lefebvre, 2021. "Moments of First-Passage Places for Jump-Diffusion Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 245-253, February.
    3. Giacomo Ascione & Yuliya Mishura & Enrica Pirozzi, 2021. "Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 53-84, March.
    4. Mario Abundo & Enrica Pirozzi, 2019. "On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes," Mathematics, MDPI, vol. 7(10), pages 1-12, October.
    5. Giuseppe D’Onofrio & Claudio Macci & Enrica Pirozzi, 2018. "Asymptotic Results for First-Passage Times of Some Exponential Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1453-1476, December.
    6. He, Yue & Kawai, Reiichiro, 2022. "Super- and subdiffusive positions in fractional Klein–Kramers equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).

    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:eee:stapro:v:205:y:2024:i:c:s0167715223001803. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.