Probability Theory and Related Fields

, Volume 94, Issue 1, pp 53–68 | Cite as

Large deviations and the propagation of chaos for Schrödinger processes

  • Robert Aebi
  • Masao Nagasawa
Article
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Revised:

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 subsetAa,b is shown, whereAa,b denotes the set of all probability measures on a path space with prescribed marginal distributions {qa, 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.

Keywords

Entropy Stochastic Process Probability Measure Probability Theory Diffusion Process 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Robert Aebi
    • 1
  • Masao Nagasawa
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceKyoto UniversityKyotoJapan
  2. 2.Institut für Angewandte Mathematik der Universität ZürichZürichSwitzerland

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