IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v35y2022i3d10.1007_s10959-021-01107-3.html
   My bibliography  Save this article

On a Theorem by A.S. Cherny for Semilinear Stochastic Partial Differential Equations

Author

Listed:
  • David Criens

    (Albert–Ludwigs–University of Freiburg)

  • Moritz Ritter

    (Albert–Ludwigs–University of Freiburg)

Abstract

We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by a cylindrical Brownian motion. The solutions are allowed to take values in Banach spaces. We show that weak uniqueness is equivalent to weak joint uniqueness, and thereby generalize a theorem by A.S. Cherny to an infinite dimensional setting. Our proof for the technical key step is different from Cherny’s and uses cylindrical martingale problems. As an application, we deduce a dual version of the Yamada–Watanabe theorem, i.e. we show that strong existence and weak uniqueness imply weak existence and strong uniqueness.

Suggested Citation

  • David Criens & Moritz Ritter, 2022. "On a Theorem by A.S. Cherny for Semilinear Stochastic Partial Differential Equations," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2052-2067, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01107-3
    DOI: 10.1007/s10959-021-01107-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-021-01107-3
    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/s10959-021-01107-3?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. G. Prato & F. Flandoli & E. Priola & M. Röckner, 2015. "Strong Uniqueness for Stochastic Evolution Equations with Unbounded Measurable Drift Term," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1571-1600, December.
    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. Wujun Lv & Xing Huang, 2021. "Harnack and Shift Harnack Inequalities for Degenerate (Functional) Stochastic Partial Differential Equations with Singular Drifts," Journal of Theoretical Probability, Springer, vol. 34(2), pages 827-851, June.
    2. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    3. David Criens, 2019. "Cylindrical Martingale Problems Associated with Lévy Generators," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1306-1359, September.
    4. Pappalettera, Umberto, 2022. "Large deviations for stochastic equations in Hilbert spaces with non-Lipschitz drift," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 1-20.

    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:35:y:2022:i:3:d:10.1007_s10959-021-01107-3. 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.