### Abstract

The large deviation principle for stochastic line integrals along Brownian paths on a compact Riemannian manifold is studied.We regard them as a random map on a Sobolev space of 1-forms.We show that the differentiability order of the Sobolev space can be chosen to be almost independent of the dimension of the underlying space by assigning higher integrability on 1-forms. The large deviation is formulated for the joint distribution of stochastic line integrals and the empirical distribution of a Brownian path. As the result, the rate function is given explicitly.

Original language | English |
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Pages (from-to) | 649-667 |

Number of pages | 19 |

Journal | Probability Theory and Related Fields |

Volume | 147 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 Jul 1 |

### Keywords

- Current-valued process
- Empirical distribution
- Large deviation
- Stochastic line integral

### ASJC Scopus subject areas

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

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## Cite this

Kusuoka, S., Kuwada, K., & Tamura, Y. (2010). Large deviation for stochastic line integrals as L

^{p}-currents.*Probability Theory and Related Fields*,*147*(3), 649-667. https://doi.org/10.1007/s00440-009-0219-5