Large deviations for Bernstein bridges

Nicolas Privault, Xiangfeng Yang and Jean-Claude Zambrini

Stochastic Processes and their Applications, 2016, vol. 126, issue 5, 1285-1305

Abstract: Bernstein processes over a finite time interval are simultaneously forward and backward Markov processes with arbitrarily fixed initial and terminal probability distributions. In this paper, a large deviation principle is proved for a family of Bernstein processes (depending on a small parameter ħ which is called the Planck constant) arising naturally in Euclidean quantum physics. The method consists in nontrivial Girsanov transformations of integral forms, suitable equivalence forms for large deviations and the (local and global) estimates on the parabolic kernel of the Schrödinger operator.

Keywords: Bernstein process; Large deviation principle; Girsanov transformation; Rate function; Schrödinger operator (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.11.003

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