IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v110y2016icp155-161.html
   My bibliography  Save this article

Small ball probabilities for a class of time-changed self-similar processes

Author

Listed:
  • Kobayashi, Kei

Abstract

This paper establishes small ball probabilities for a class of time-changed processes X∘E, where X is a self-similar process and E is an independent continuous process, each with a certain small ball probability. In particular, examples of the outer process X and the time change E include an iterated fractional Brownian motion and the inverse of a general subordinator with infinite Lévy measure, respectively. The small ball probabilities of such time-changed processes show power law decay, and the rate of decay does not depend on the small deviation order of the outer process X, but on the self-similarity index of X.

Suggested Citation

  • Kobayashi, Kei, 2016. "Small ball probabilities for a class of time-changed self-similar processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 155-161.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:155-161
    DOI: 10.1016/j.spl.2015.12.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215301218
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.12.024?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. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    2. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    3. Nane, Erkan, 2009. "Laws of the iterated logarithm for a class of iterated processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1744-1751, August.
    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. Kei Kobayashi & Hyunchul Park, 2023. "Spectral Heat Content for Time-Changed Killed Brownian Motions," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1148-1180, June.

    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. Gajda, Janusz & Magdziarz, Marcin, 2014. "Large deviations for subordinated Brownian motion and applications," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 149-156.
    2. Kerger, Phillip & Kobayashi, Kei, 2020. "Parameter estimation for one-sided heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 164(C).
    3. Meerschaert, Mark M. & Toaldo, Bruno, 2019. "Relaxation patterns and semi-Markov dynamics," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2850-2879.
    4. Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.
    5. P. Escalona & F. Ordóñez & I. Kauak, 2017. "Critical level rationing in inventory systems with continuously distributed demand," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 273-301, January.
    6. Magdziarz, M. & Scheffler, H.P. & Straka, P. & Zebrowski, P., 2015. "Limit theorems and governing equations for Lévy walks," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4021-4038.
    7. Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
    8. Hainaut, Donatien & Leonenko, Nikolai, 2020. "Option pricing in illiquid markets: a fractional jump-diffusion approach," LIDAM Discussion Papers ISBA 2020003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
    10. Kei Kobayashi & Hyunchul Park, 2023. "Spectral Heat Content for Time-Changed Killed Brownian Motions," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1148-1180, June.
    11. Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2022. "Non-local Solvable Birth–Death Processes," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1284-1323, June.
    12. Kondratiev, Yuri & da Silva, José L., 2023. "Compound Poisson processes: Potentials, Green measures and random times," Statistics & Probability Letters, Elsevier, vol. 197(C).
    13. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.
    14. Kevin Z. Tong & Allen Liu, 2019. "Option pricing in a subdiffusive constant elasticity of variance (CEV) model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-21, June.
    15. Prakash, Amit & Kaur, Hardish, 2017. "Numerical solution for fractional model of Fokker-Planck equation by using q-HATM," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 99-110.
    16. Dupret, Jean-Loup & Hainaut, Donatien, 2022. "A subdiffusive stochastic volatility jump model," LIDAM Discussion Papers ISBA 2022001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Beghin, Luisa & Macci, Claudio & Ricciuti, Costantino, 2020. "Random time-change with inverses of multivariate subordinators: Governing equations and fractional dynamics," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6364-6387.
    18. Torricelli, Lorenzo, 2020. "Trade duration risk in subdiffusive financial models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    19. A. Kumar & J. Gajda & A. Wyłomańska & R. Połoczański, 2019. "Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 185-202, March.
    20. Qing Tang & Fabio Camilli, 2020. "Variational Time-Fractional Mean Field Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 573-588, June.

    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:110:y:2016:i:c:p:155-161. 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.