IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v191y2026ics0304414925002315.html

Homeomorphism of the Revuz correspondence for finite energy integrals

Author

Listed:
  • Ooi, Takumu

Abstract

We provide necessary and sufficient conditions for the convergence of Revuz measures of finite energy integrals. More precisely, the Revuz map from the set of all smooth measures of finite energy integrals, equipped with the topology induced by the norm given by the sum of the Dirichlet form and the L2(m)-norm, to the space of positive continuous additive functionals, equipped with the topology induced by the L2(Pm+κ+ν0)-norm with the local uniform topology, is a homeomorphism, where m is the underlying measure, κ is the killing measure of a Dirichlet form and ν0 is an energy functional corresponding to the part of the process that continuously escapes to the cemetery point.

Suggested Citation

  • Ooi, Takumu, 2026. "Homeomorphism of the Revuz correspondence for finite energy integrals," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925002315
    DOI: 10.1016/j.spa.2025.104787
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925002315
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104787?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

    for a different version of it.

    References listed on IDEAS

    as
    1. P. J. Fitzsimmons & R. K. Getoor, 1996. "Smooth measures and continuous additive functionals of right Markov processes," Springer Books, in: Nobuyuki Ikeda & Shinzo Watanabe & Masatoshi Fukushima & Hiroshi Kunita (ed.), Itô’s Stochastic Calculus and Probability Theory, pages 31-49, Springer.
    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.

      More about this item

      Keywords

      ;
      ;
      ;

      Statistics

      Access and download statistics

      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:191:y:2026:i:c:s0304414925002315. 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.