IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v32y2019i4d10.1007_s10959-018-0857-6.html
   My bibliography  Save this article

On the Favorite Points of Symmetric Lévy Processes

Author

Listed:
  • Bo Li

    (Central China Normal University)

  • Yimin Xiao

    (Michigan State University)

  • Xiaochuan Yang

    (Michigan State University)

Abstract

This paper is concerned with asymptotic behavior (at zero and at infinity) of the favorite points of Lévy processes. By exploring Molchan’s idea for deriving lower tail probabilities of Gaussian processes with stationary increments, we extend the result of Marcus (J Theor Probab 14(3):867–885, 2001) on the favorite points to a larger class of symmetric Lévy processes.

Suggested Citation

  • Bo Li & Yimin Xiao & Xiaochuan Yang, 2019. "On the Favorite Points of Symmetric Lévy Processes," Journal of Theoretical Probability, Springer, vol. 32(4), pages 1943-1972, December.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:4:d:10.1007_s10959-018-0857-6
    DOI: 10.1007/s10959-018-0857-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-018-0857-6
    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/s10959-018-0857-6?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. Shen, Yi, 2016. "Random locations, ordered random sets and stationarity," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 906-929.
    2. Eisenbaum, Nathalie & Kaspi, Haya, 2009. "On permanental processes," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1401-1415, May.
    3. René L. Schilling, 1998. "Feller Processes Generated by Pseudo-Differential Operators: On the Hausdorff Dimension of Their Sample Paths," Journal of Theoretical Probability, Springer, vol. 11(2), pages 303-330, April.
    4. Berman, Simeon M., 1987. "Spectral conditions for local nondeterminism," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 73-84.
    5. Michael B. Marcus, 2001. "The Most Visited Sites of Certain Lévy Processes," Journal of Theoretical Probability, Springer, vol. 14(3), pages 867-885, July.
    6. Eisenbaum, Nathalie & Khoshnevisan, Davar, 2002. "On the most visited sites of symmetric Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 241-256, October.
    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. Wu, Dongsheng & Xiao, Yimin, 2009. "Continuity in the Hurst index of the local times of anisotropic Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1823-1844, June.
    2. Marcus, Michael B. & Rosen, Jay, 2020. "Permanental sequences related to a Markov chain example of Kolmogorov," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7098-7130.
    3. Kozubowski, Tomasz J. & Mazur, Stepan & Podgórski, Krzysztof, 2022. "Matrix Gamma Distributions and Related Stochastic Processes," Working Papers 2022:12, Örebro University, School of Business.
    4. Xiaochuan Yang, 2018. "Hausdorff Dimension of the Range and the Graph of Stable-Like Processes," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2412-2431, December.
    5. Kogan, Hana & Marcus, Michael B., 2012. "Permanental vectors," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1226-1247.
    6. Shen, Jie & Shen, Yi & Wang, Ruodu, 2019. "Random locations of periodic stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 878-901.
    7. Chen, Dayue & de Raphélis, Loïc & Hu, Yueyun, 2018. "Favorite sites of randomly biased walks on a supercritical Galton–Watson tree," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1525-1557.
    8. Eisenbaum, Nathalie, 2012. "Stochastic order for alpha-permanental point processes," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 952-967.
    9. D. Baraka & T. S. Mountford, 2011. "The Exact Hausdorff Measure of the Zero Set of Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 24(1), pages 271-293, March.
    10. Kurt, Kevin & Frey, Rüdiger, 2022. "Markov-modulated affine processes," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 391-422.

    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:jotpro:v:32:y:2019:i:4:d:10.1007_s10959-018-0857-6. 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.