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Large deviations and the propagation of chaos for Schrödinger processes


Aebi, R; Nagasawa, M (1992). Large deviations and the propagation of chaos for Schrödinger processes. Probability Theory and Related Fields, 94(1):53-68.

Abstract

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.

Abstract

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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7 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1992
Deposited On:29 Nov 2010 16:29
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0178-8051
Publisher DOI:https://doi.org/10.1007/BF01222509
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1189085
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0767.60056

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