IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v21y2008i1d10.1007_s10959-007-0104-z.html
   My bibliography  Save this article

Towards a Characterization of Markov Processes Enjoying the Time-Inversion Property

Author

Listed:
  • Stephan Lawi

    (Université Paris VI & Université Paris VII)

Abstract

We give a necessary and sufficient condition for a homogeneous Markov process taking values in ℝ n to enjoy the time-inversion property of degree α. The condition sets the shape for the semigroup densities of the process and allows to further extend the class of known processes satisfying the time-inversion property. As an application we recover the result of Watanabe (Z. Wahrscheinlichkeitstheor. Verwandte Geb. 31:115–124, 1975) for continuous and conservative Markov processes on ℝ+. As new examples we generalize Dunkl processes and construct a matrix-valued process with jumps related to the Wishart process by a skew-product representation.

Suggested Citation

  • Stephan Lawi, 2008. "Towards a Characterization of Markov Processes Enjoying the Time-Inversion Property," Journal of Theoretical Probability, Springer, vol. 21(1), pages 144-168, March.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:1:d:10.1007_s10959-007-0104-z
    DOI: 10.1007/s10959-007-0104-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-007-0104-z
    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/s10959-007-0104-z?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. Bru, Marie-France, 1989. "Diffusions of perturbed principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 127-136, April.
    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. Mayerhofer, Eberhard & Pfaffel, Oliver & Stelzer, Robert, 2011. "On strong solutions for positive definite jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2072-2086, September.
    2. Song, Jian & Yao, Jianfeng & Yuan, Wangjun, 2022. "Recent advances on eigenvalues of matrix-valued stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Carlos G. Pacheco, 2016. "Picard Iterations for Diffusions on Symmetric Matrices," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1444-1457, December.
    4. Nourdin, Ivan & Pu, Fei, 2022. "Gaussian fluctuation for Gaussian Wishart matrices of overall correlation," Statistics & Probability Letters, Elsevier, vol. 181(C).
    5. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    6. Nualart, David & Pérez-Abreu, Victor, 2014. "On the eigenvalue process of a matrix fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4266-4282.
    7. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    8. Benjamin Jourdain & Ezéchiel Kahn, 2022. "Strong Solutions to a Beta-Wishart Particle System," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1574-1613, September.
    9. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Trinh, Hoang Dung & Trinh, Khanh Duy, 2021. "Beta Laguerre processes in a high temperature regime," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 192-205.

    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:jotpro:v:21:y:2008:i:1:d:10.1007_s10959-007-0104-z. 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.