IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v17y1993i5p369-375.html
   My bibliography  Save this article

Note on the Schrödinger equation and I-projections

Author

Listed:
  • Rüschendorf, L.
  • Thomsen, W.

Abstract

We determine sufficient conditions for the closedness of sum spaces of L1-functions. As a consequence of Csiszar's projection theorem this implies generalizations of results of Fortet, Beurling and Hobby and Pyke on the existence and uniqueness of solutions of some nonlinear integral equations, which were introduced by Schrödinger, to describe the most probably behaviour of Brownian motions conditional on the observed initial and final state in a finite interval (0, t1). The results is also of interest for a large deviation formula for infinite dimensional Brownian motions related to Schrödinger bridges and for the construction of optimal estimators in marginal models.

Suggested Citation

  • Rüschendorf, L. & Thomsen, W., 1993. "Note on the Schrödinger equation and I-projections," Statistics & Probability Letters, Elsevier, vol. 17(5), pages 369-375, August.
  • Handle: RePEc:eee:stapro:v:17:y:1993:i:5:p:369-375
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(93)90257-J
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gramer Erhard, 2000. "Probability Measures With Given Marginals And Conditionals: I-Projections And Conditional Iterative Proportional Fitting," Statistics & Risk Modeling, De Gruyter, vol. 18(3), pages 311-330, March.
    2. Mikami, Toshio & Thieullen, Michèle, 2006. "Duality theorem for the stochastic optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1815-1835, December.
    3. Hà Quang Minh, 2023. "Entropic Regularization of Wasserstein Distance Between Infinite-Dimensional Gaussian Measures and Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 36(1), pages 201-296, March.
    4. Geenens Gery, 2020. "Copula modeling for discrete random vectors," Dependence Modeling, De Gruyter, vol. 8(1), pages 417-440, January.
    5. Geenens Gery, 2020. "Copula modeling for discrete random vectors," Dependence Modeling, De Gruyter, vol. 8(1), pages 417-440, January.
    6. Marcel Nutz & Johannes Wiesel & Long Zhao, 2023. "Martingale Schrödinger bridges and optimal semistatic portfolios," Finance and Stochastics, Springer, vol. 27(1), pages 233-254, January.
    7. Butucea, Cristina & Delmas, Jean-François & Dutfoy, Anne & Fischer, Richard, 2015. "Maximum entropy copula with given diagonal section," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 61-81.
    8. Friedrich Pukelsheim, 2014. "Biproportional scaling of matrices and the iterative proportional fitting procedure," Annals of Operations Research, Springer, vol. 215(1), pages 269-283, April.
    9. Toshio Mikami, 2021. "Stochastic optimal transport revisited," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-26, February.

    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:stapro:v:17:y:1993:i:5:p:369-375. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/622892/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.