## Abstract

We prove a precision of large deviation principle for current-valued processes such as shown in Bolthausen et al. (Ann Probab 23(1):236-267, 1995) for mean empirical measures. The class of processes we consider is determined by the martingale part of stochastic line integrals of 1-forms on a compact Riemannian manifold. For the pair of the current-valued process and mean empirical measures, we give an asymptotic evaluation of a nonlinear Laplace transform under a nondegeneracy assumption on the Hessian of the exponent at equilibrium states. As a direct consequence, our result implies the Laplace approximation for stochastic line integrals or periodic diffusions. In particular, we recover a result in Bolthausen et al. (Ann Probab 23(1):236-267, 1995) in our framework.

Original language | English |
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Pages (from-to) | 1-51 |

Number of pages | 51 |

Journal | Probability Theory and Related Fields |

Volume | 144 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2009 May |

Externally published | Yes |

## Keywords

- Empirical measure
- Laplace approximation
- Large deviation
- Stochastic line integral

## ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty