IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v88y2014icp149-156.html
   My bibliography  Save this article

Large deviations for subordinated Brownian motion and applications

Author

Listed:
  • Gajda, Janusz
  • Magdziarz, Marcin

Abstract

This paper concerns the problem of large deviation for the subordinated process ZH(t)=WH(T(t)). The process WH={WH(t),t∈R} is the fractional Brownian motion with Hurst index H∈(0,1) taking values in R. T={T(t),t≥0} is the inverse α-stable subordinator. In this paper we extend the results obtained in M.M. Meerschaert et al. (2008) to the whole range of parameter α∈(0,1).

Suggested Citation

  • Gajda, Janusz & Magdziarz, Marcin, 2014. "Large deviations for subordinated Brownian motion and applications," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 149-156.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:149-156
    DOI: 10.1016/j.spl.2014.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214000522
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.02.003?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. 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.
    2. Bañuelos, Rodrigo & DeBlassie, Dante, 2006. "The exit distribution for iterated Brownian motion in cones," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 36-69, January.
    3. Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 1995. "Global Strassen-type theorems for iterated Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 59(2), pages 321-341, October.
    4. Nane, Erkan, 2008. "Isoperimetric-type inequalities for iterated Brownian motion in," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 90-95, January.
    5. 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.
    6. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
    7. Nane, Erkan, 2006. "Iterated Brownian motion in bounded domains in," Stochastic Processes and their Applications, Elsevier, vol. 116(6), pages 905-916, 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. Gajda, J. & Wyłomańska, A. & Kantz, H. & Chechkin, A.V. & Sikora, G., 2018. "Large deviations of time-averaged statistics for Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 47-55.

    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. 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.
    2. 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.
    3. Karipova, Gulnur & Magdziarz, Marcin, 2017. "Pricing of basket options in subdiffusive fractional Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 245-253.
    4. 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.
    5. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    6. Hainaut, Donatien, 2020. "Fractional Hawkes processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    7. 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.
    8. Ketelbuters, John-John & Hainaut, Donatien, 2022. "CDS pricing with fractional Hawkes processes," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1139-1150.
    9. Foad Shokrollahi & Adem Kılıçman & Marcin Magdziarz, 2016. "Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-22, March.
    10. Golder, J. & Joelson, M. & Néel, M.C., 2011. "Mass transport with sorption in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2181-2189.
    11. 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.
    12. 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).
    13. Lv, Longjin & Xiao, Jianbin & Fan, Liangzhong & Ren, Fuyao, 2016. "Correlated continuous time random walk and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 100-107.
    14. 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.
    15. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
    16. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    17. 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.
    18. 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.
    19. 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).
    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:88:y:2014:i:c:p:149-156. 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.