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Large deviations and the propagation of chaos for Schrödinger processes
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  • Published: March 1992

Large deviations and the propagation of chaos for Schrödinger processes

  • Robert Aebi1 nAff2 &
  • Masao Nagasawa2 

Probability Theory and Related Fields volume 94, pages 53–68 (1992)Cite this article

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Summary

Schrödinger processes due to Schrödinger (1931) (the definition of which is given in Sect. 4) are uniquely characterized by a large deviation principle, in terms of the relative entropy with respect to a reference process, which is a renormalized diffusion process with creation and killing in applications. Anapproximate Sanov property of a subsetA a,b is shown, whereA a,b denotes the set of all probability measures on a path space with prescribed marginal distributions {q a, qb} at finite initial and terminal timesa andb, respectively. It is shown that there exists the unique Markovian modification ofn-independent copies of renormalized processes conditioned by the empirical distribution, and that the propagation of chaos holds for the system of interacting particles with the Schrödinger process as the limiting distribution.

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Author information

Author notes
  1. Robert Aebi

    Present address: Department of Mathematics and Statistics, James Clark Maxwell Building, the King's Buildings, Mayfield Road, EH93JZ, Edinburgh, UK

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kyoto University, 606, Kyoto, Japan

    Robert Aebi

  2. Institut für Angewandte Mathematik der Universität Zürich, Rämistrasse 74, CH-8001, Zürich, Switzerland

    Masao Nagasawa

Authors
  1. Robert Aebi
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  2. Masao Nagasawa
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Aebi, R., Nagasawa, M. Large deviations and the propagation of chaos for Schrödinger processes. Probab. Th. Rel. Fields 94, 53–68 (1992). https://doi.org/10.1007/BF01222509

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  • Received: 21 December 1990

  • Revised: 01 January 1992

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01222509

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Keywords

  • Entropy
  • Stochastic Process
  • Probability Measure
  • Probability Theory
  • Diffusion Process
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