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Large deviations and the propagation of chaos for Schrödinger processes. (English) Zbl 0767.60056

Summary: Schrödinger processes due to E. Schrödinger [Ann. Inst. H. Poincaré 2, 269-310 (1932; Zbl 0004.42505)]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. An approximate Sanov property of a subset \(A_{a,b}\) is shown, where \(A_{a,b}\) denotes the set of all probability measures on a path space with prescribed marginal distributions \(\{q_ a,q_ b\}\) at finite initial and terminal times \(a\) and \(b\), respectively. It is shown that there exists the unique Markovian modification of \(n\)-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.

MSC:

60H25 Random operators and equations (aspects of stochastic analysis)
60K40 Other physical applications of random processes
60F10 Large deviations

Citations:

Zbl 0004.42505
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