Large deviation for stochastic line integrals as Lp-currents

Shigeo Kusuoka, Kazumasa Kuwada, Yozo Tamura

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)649-667
Number of pages19
JournalProbability Theory and Related Fields
Volume147
Issue number3
DOIs
Publication statusPublished - 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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