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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
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    Citations

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    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.

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