IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i1d10.1007_s11009-018-9648-x.html
   My bibliography  Save this article

Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators

Author

Listed:
  • A. Kumar

    (Indian Institute of Technology Ropar)

  • J. Gajda

    (Wrocław University of Science and Technology)

  • A. Wyłomańska

    (Wrocław University of Science and Technology)

  • R. Połoczański

    (Wrocław University of Science and Technology)

Abstract

In recent years subordinated processes have been widely considered in the literature. These processes not only have wide applications but also have interesting theoretical properties. In this paper we consider fractional Brownian motion (FBM) time-changed by two processes, tempered stable and inverse tempered stable. We present main properties of the subordinated FBM such as long range dependence and associated fractional partial differential equations for the probability density functions. Moreover, we present how to simulate both subordinated processes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9648-x
    DOI: 10.1007/s11009-018-9648-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9648-x
    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/s11009-018-9648-x?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. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    2. Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
    3. Sato, Ken-iti, 2001. "Subordination and self-decomposability," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 317-324, October.
    4. 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.
    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. Luisa Beghin & Roberto Garra, 2019. "A Note on the Generalized Relativistic Diffusion Equation," Mathematics, MDPI, vol. 7(11), pages 1-9, October.
    2. 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.

    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. 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.
    2. Di Nardo, E. & Marena, M. & Semeraro, P., 2020. "On non-linear dependence of multivariate subordinated Lévy processes," Statistics & Probability Letters, Elsevier, vol. 166(C).
    3. 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.
    4. Gupta, Neha & Kumar, Arun, 2022. "Inverse tempered stable subordinators and related processes with Mellin transform," Statistics & Probability Letters, Elsevier, vol. 186(C).
    5. 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.
    6. Arun Kumar & Palaniappan Vellaisamy, 2012. "Fractional Normal Inverse Gaussian Process," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 263-283, June.
    7. Torricelli, Lorenzo, 2020. "Trade duration risk in subdiffusive financial models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    8. Choe, Geon Ho & Lee, Dong Min, 2016. "Numerical computation of hitting time distributions of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 289-294.
    9. Vladimir Panov, 2017. "Series Representations for Multivariate Time-Changed Lévy Models," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 97-119, March.
    10. Petar Jevtić & Marina Marena & Patrizia Semeraro, 2019. "Multivariate Marked Poisson Processes And Market Related Multidimensional Information Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-26, March.
    11. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    12. Brian Sing Fan Chan & Andy Cheuk Hin Cheng & Alfred Ka Chun Ma, 2018. "Stock Market Volatility and Trading Volume: A Special Case in Hong Kong With Stock Connect Turnover," JRFM, MDPI, vol. 11(4), pages 1-17, October.
    13. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    14. Mende, Alexander, 2005. "09/11 on the USD/EUR Foreign Exchange Market," Hannover Economic Papers (HEP) dp-312, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    15. Härdle, Wolfgang Karl & Hautsch, Nikolaus & Pigorsch, Uta, 2008. "Measuring and modeling risk using high-frequency data," SFB 649 Discussion Papers 2008-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    16. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    17. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    18. Cornelis A. Los, 2004. "Nonparametric Efficiency Testing of Asian Stock Markets Using Weekly Data," Finance 0409033, University Library of Munich, Germany.
    19. Konishi, Hizuru, 2002. "Optimal slice of a VWAP trade," Journal of Financial Markets, Elsevier, vol. 5(2), pages 197-221, April.
    20. Michelle B Graczyk & Sílvio M Duarte Queirós, 2017. "Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-23, July.

    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:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9648-x. 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.