IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v72y1997i2p265-287.html
   My bibliography  Save this article

On Markov properties of Lévy waves in two dimensions

Author

Listed:
  • Dalang, Robert C.
  • Hou, Qiang

Abstract

Markov properties of the solution to the wave equation in two spatial dimensions driven by a Lévy point process are considered. When the velocity of waves is 1, then for domains bounded by a plane, the sharp Markov property is shown to hold if and only if the angle between the plane and the time axis is at least [pi]/4. The sharp Markov property also holds for domains that are bounded polyhedra, because the boundary sigma-field is extremely large. The same is true of the germ-field of the boundary of a bounded open set, and this implies the germ-field Markov property for these sets.

Suggested Citation

  • Dalang, Robert C. & Hou, Qiang, 1997. "On Markov properties of Lévy waves in two dimensions," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 265-287, December.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:2:p:265-287
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00087-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Dalang, Robert C. & Russo, Francesco, 1988. "A prediction problem for the Brownian sheet," Journal of Multivariate Analysis, Elsevier, vol. 26(1), pages 16-47, July.
    2. Ferrante, Marco & Nualart, David, 1994. "On the Markov property of a stochastic difference equation," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 239-250, August.
    3. Adler, R. J. & Monrad, D. & Scissors, R. H. & Wilson, R., 1983. "Representations, decompositions and sample function continuity of random fields with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 3-30, June.
    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. Herbin, Erick & Merzbach, Ely, 2013. "The set-indexed Lévy process: Stationarity, Markov and sample paths properties," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1638-1670.
    2. Dalang, Robert C. & Khoshnevisan, Davar, 2004. "Recurrent lines in two-parameter isotropic stable Lévy sheets," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 81-107, November.
    3. Balan, Raluca M. & Tudor, Ciprian A., 2010. "The stochastic wave equation with fractional noise: A random field approach," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2468-2494, December.

    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. Francesco Iafrate & Costantino Ricciuti, 2024. "Some Families of Random Fields Related to Multiparameter Lévy Processes," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3055-3088, November.
    2. Hannebicque, Brice & Herbin, Érick, 2022. "Regularity of an abstract Wiener integral," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 154-196.
    3. Fageot, Julien & Humeau, Thomas, 2021. "The domain of definition of the Lévy white noise," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 75-102.
    4. Sauri, Orimar & Veraart, Almut E.D., 2017. "On the class of distributions of subordinated Lévy processes and bases," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 475-496.
    5. Balan, R. M., 2002. "Set-indexed processes with independent increments," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 415-424, October.
    6. Lagaize, Sandrine, 2001. "Hölder Exponent for a Two-Parameter Lévy Process," Journal of Multivariate Analysis, Elsevier, vol. 77(2), pages 270-285, May.
    7. Baccin, Maria C. & Ferrante, Marco, 1995. "On a stochastic delay difference equation with boundary conditions and its Markov property," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 131-146, November.
    8. Zapala, August M., 2003. "A criterion for right continuity of filtrations generated by group-valued additive processes," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 79-87, May.
    9. Herbin, Erick & Merzbach, Ely, 2013. "The set-indexed Lévy process: Stationarity, Markov and sample paths properties," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1638-1670.

    More about this item

    Keywords

    60G60 60H15;

    JEL classification:

    Statistics

    Access and download statistics

    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:spapps:v:72:y:1997:i:2:p:265-287. 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/505572/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.