IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v29y2016i3d10.1007_s10959-015-0594-z.html
   My bibliography  Save this article

Time Regularity of Generalized Ornstein–Uhlenbeck Processes with Lévy Noises in Hilbert Spaces

Author

Listed:
  • Yong Liu

    (Peking University)

  • Jianliang Zhai

    (University of Science and Technology of China)

Abstract

In this paper we first obtain a necessary condition for $$H$$ H -càdlàg modification and $$H$$ H -weakly càdlàg modification of generalized Ornstein–Uhlenbeck processes with Lévy noises in Hilbert spaces $$H$$ H . Then we give a necessary and sufficient condition for the $$H$$ H -càdlàg modification and $$H$$ H -weakly càdlàg modification of Ornstein–Uhlenbeck processes driven by cylindrical $$\alpha $$ α -semistable processes. Secondly, we investigate the properties of cylindrical càdlàg modification and $$V$$ V -cylindrical càdlàg modification. Applying the obtained results to diagonal Ornstein–Uhlenbeck processes with $$\alpha $$ α -stable noises, we show a necessary and sufficient condition for cylindrical càdlàg modification and $$V$$ V -cylindrical càdlàg modification in the symmetric case for $$\alpha \in (0,1)$$ α ∈ ( 0 , 1 ) and give a sufficient condition in the general case for $$\alpha \in (0,2)$$ α ∈ ( 0 , 2 ) . Some examples illustrate the relations among the concepts of various càdlàg modifications.

Suggested Citation

  • Yong Liu & Jianliang Zhai, 2016. "Time Regularity of Generalized Ornstein–Uhlenbeck Processes with Lévy Noises in Hilbert Spaces," Journal of Theoretical Probability, Springer, vol. 29(3), pages 843-866, September.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:3:d:10.1007_s10959-015-0594-z
    DOI: 10.1007/s10959-015-0594-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-015-0594-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/s10959-015-0594-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. Peszat, S. & Zabczyk, J., 2013. "Time regularity of solutions to linear equations with Lévy noise in infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 719-751.
    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. Tomasz Kosmala & Markus Riedle, 2021. "Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators," Journal of Theoretical Probability, Springer, vol. 34(1), pages 477-497, March.
    2. Leahy, James-Michael & Mikulevičius, Remigijus, 2015. "On degenerate linear stochastic evolution equations driven by jump processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3748-3784.

    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:29:y:2016:i:3:d:10.1007_s10959-015-0594-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.