IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i4p2471-2487.html
   My bibliography  Save this article

From infinite urn schemes to self-similar stable processes

Author

Listed:
  • Durieu, Olivier
  • Samorodnitsky, Gennady
  • Wang, Yizao

Abstract

We investigate the randomized Karlin model with parameter β∈(0,1), which is based on an infinite urn scheme. It has been shown before that when the randomization is bounded, the so-called odd-occupancy process scales to a fractional Brownian motion with Hurst index β∕2∈(0,1∕2). We show here that when the randomization is heavy-tailed with index α∈(0,2), then the odd-occupancy process scales to a (β∕α)-self-similar symmetric α-stable process with stationary increments.

Suggested Citation

  • Durieu, Olivier & Samorodnitsky, Gennady & Wang, Yizao, 2020. "From infinite urn schemes to self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2471-2487.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:2471-2487
    DOI: 10.1016/j.spa.2019.07.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918303843
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.07.008?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. Lei, Pedro & Nualart, David, 2009. "A decomposition of the bifractional Brownian motion and some applications," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 619-624, March.
    2. Alsmeyer, Gerold & Iksanov, Alexander & Marynych, Alexander, 2017. "Functional limit theorems for the number of occupied boxes in the Bernoulli sieve," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 995-1017.
    3. Pipiras,Vladas & Taqqu,Murad S., 2017. "Long-Range Dependence and Self-Similarity," Cambridge Books, Cambridge University Press, number 9781107039469, October.
    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. Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.
    2. Iksanov, Alexander & Kotelnikova, Valeriya, 2022. "Small counts in nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 283-320.

    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. Yuanhua Feng & Wolfgang Karl Härdle, 2021. "Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression," Working Papers CIE 142, Paderborn University, CIE Center for International Economics.
    2. Bondarenko, Valeria & Bondarenko, Victor & Truskovskyi, Kyryl, 2017. "Forecasting of time data with using fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 44-50.
    3. Ran Wang & Yimin Xiao, 2022. "Exact Uniform Modulus of Continuity and Chung’s LIL for the Generalized Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2442-2479, December.
    4. Grahovac, Danijel & Leonenko, Nikolai N. & Taqqu, Murad S., 2018. "Intermittency of trawl processes," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 235-242.
    5. Nourdin, Ivan & Nualart, David & Peccati, Giovanni, 2021. "The Breuer–Major theorem in total variation: Improved rates under minimal regularity," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 1-20.
    6. Battey, H.S. & Cox, D.R., 2022. "Some aspects of non-standard multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Harnett, Daniel & Nualart, David, 2012. "Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3460-3505.
    8. Patrice Abry & Yannick Malevergne & Herwig Wendt & Marc Senneret & Laurent Jaffrès & Blaise Liaustrat, 2019. "Shuffling for understanding multifractality, application to asset price time series," Post-Print hal-02361738, HAL.
    9. Kubiv Stepan, 2019. "Approximations and forecasting quasi-stationary processes with sudden runs," Technology audit and production reserves, 4(48) 2019, Socionet;Technology audit and production reserves, vol. 4(4(48)), pages 37-39.
    10. Zuopeng Fu & Yizao Wang, 2020. "Stable Processes with Stationary Increments Parameterized by Metric Spaces," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1737-1754, September.
    11. Grahovac, Danijel, 2022. "Intermittency in the small-time behavior of Lévy processes," Statistics & Probability Letters, Elsevier, vol. 187(C).
    12. Baek, Changryong & Gates, Katheleen M. & Leinwand, Benjamin & Pipiras, Vladas, 2021. "Two sample tests for high-dimensional autocovariances," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    13. Johann Gehringer & Xue-Mei Li, 2022. "Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process," Journal of Theoretical Probability, Springer, vol. 35(1), pages 426-456, March.
    14. Obayda Assaad & Ciprian A. Tudor, 2020. "Parameter identification for the Hermite Ornstein–Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 251-270, July.
    15. Tomoyuki Ichiba & Guodong Pang & Murad S. Taqqu, 2022. "Path Properties of a Generalized Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(1), pages 550-574, March.
    16. Meng-Chen Hsieh & Clifford Hurvich & Philippe Soulier, 2022. "Long-Horizon Return Predictability from Realized Volatility in Pure-Jump Point Processes," Papers 2202.00793, arXiv.org.
    17. Gannaz, Irène, 2023. "Asymptotic normality of wavelet covariances and multivariate wavelet Whittle estimators," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 485-534.
    18. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    19. Abry, Patrice & Didier, Gustavo, 2018. "Wavelet eigenvalue regression for n-variate operator fractional Brownian motion," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 75-104.
    20. Araya, Héctor & Tudor, Ciprian A., 2019. "Behavior of the Hermite sheet with respect to theHurst index," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2582-2605.

    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:130:y:2020:i:4:p:2471-2487. 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.