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Large deviations for Bernstein bridges

Author

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  • Privault, Nicolas
  • Yang, Xiangfeng
  • Zambrini, Jean-Claude

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.

Suggested Citation

  • Privault, Nicolas & Yang, Xiangfeng & Zambrini, Jean-Claude, 2016. "Large deviations for Bernstein bridges," Stochastic Processes and their Applications, Elsevier, vol. 126(5), pages 1285-1305.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:5:p:1285-1305
    DOI: 10.1016/j.spa.2015.11.003
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    References listed on IDEAS

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    1. Wittich, O., 2005. "An explicit local uniform large deviation bound for Brownian bridges," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 51-56, June.
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