IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v120y2010i12p2363-2389.html
   My bibliography  Save this article

[alpha]-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes

Author

Listed:
  • Maejima, Makoto
  • Ueda, Yohei

Abstract

The concept of selfdecomposability has been generalized to that of [alpha]-selfdecomposability, , by many authors. We first mention the existing results on the class of [alpha]-selfdecomposable distributions and investigate the remaining problems. We give complete characterizations by stochastic integrals with respect to Lévy processes for the case 1

Suggested Citation

  • Maejima, Makoto & Ueda, Yohei, 2010. "[alpha]-selfdecomposable distributions and related Ornstein-Uhlenbeck type processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2363-2389, December.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:12:p:2363-2389
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00191-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Wolfe, Stephen James, 1982. "On a continuous analogue of the stochastic difference equation Xn=[rho]Xn-1+Bn," Stochastic Processes and their Applications, Elsevier, vol. 12(3), pages 301-312, May.
    2. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self‐Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57, January.
    3. repec:dau:papers:123456789/1380 is not listed on IDEAS
    4. Jurek, Zbigniew J. & Schreiber, Bertram M., 1992. "Fourier transforms of measures from the classes [beta]' -2," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 194-211, May.
    5. Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
    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. Zheng, Jing & Lin, Zhengyan & Tong, Changqing, 2009. "The Hausdorff dimension of the range for the Markov processes of Ornstein–Uhlenbeck type," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2008-2013.
    2. Brockwell, Peter J. & Lindner, Alexander, 2015. "Prediction of Lévy-driven CARMA processes," Journal of Econometrics, Elsevier, vol. 189(2), pages 263-271.
    3. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    4. Jan-Frederik Mai & Steffen Schenk & Matthias Scherer, 2017. "Two Novel Characterizations of Self-Decomposability on the Half-Line," Journal of Theoretical Probability, Springer, vol. 30(1), pages 365-383, March.
    5. Patrizia Semeraro, 2022. "Multivariate tempered stable additive subordination for financial models," Mathematics and Financial Economics, Springer, volume 16, number 3, June.
    6. Dilip B. Madan & King Wang, 2022. "Two sided efficient frontiers at multiple time horizons," Annals of Finance, Springer, vol. 18(3), pages 327-353, September.
    7. Albrecher, Hansjoerg & Guillaume, Florence & Schoutens, Wim, 2013. "Implied liquidity: Model sensitivity," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 48-67.
    8. Pérez-Abreu, Victor & Stelzer, Robert, 2014. "Infinitely divisible multivariate and matrix Gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 155-175.
    9. Zorana Grbac & David Krief & Peter Tankov, 2015. "Approximate Option Pricing in the L\'evy Libor Model," Papers 1511.08466, arXiv.org, revised Jul 2016.
    10. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
    11. Dilip Madan, 2011. "Joint risk-neutral laws and hedging," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 840-850.
    12. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    13. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.
    14. T. Ogihara & N. Yoshida, 2011. "Quasi-likelihood analysis for the stochastic differential equation with jumps," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 189-229, October.
    15. Barndorff-Nielsen, Ole E. & Maejima, Makoto, 2008. "Semigroups of Upsilon transformations," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2334-2343, December.
    16. Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    17. Arturo Kohatsu & Makoto Yamazato, 2003. "On moments and tail behaviors of storage processes," Economics Working Papers 673, Department of Economics and Business, Universitat Pompeu Fabra.
    18. Brockwell, Peter J. & Lindner, Alexander, 2009. "Existence and uniqueness of stationary Lévy-driven CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2660-2681, August.
    19. Möhle, Martin & Vetter, Benedict, 2023. "Scaling limits for a class of regular Ξ-coalescents," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 387-422.
    20. Dilip B. Madan, 2016. "Adapted hedging," Annals of Finance, Springer, vol. 12(3), pages 305-334, December.

    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:120:y:2010:i:12:p:2363-2389. 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.