An infinite dimensional central limit theorem for correlated martingales

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Abstract

The paper derives a functional central limit theorem for the empirical distributions of a system of strongly correlated continuous martingales at the level of the full trajectory space. We provide a general class of functionals for which the weak convergence to a centered Gaussian random field takes place. An explicit formula for the covariance is established and a characterization of the limit is given in terms of an inductive system of SPDEs. We also show a density theorem for a Sobolev-type class of functionals on the space of continuous functions.

Original languageEnglish (US)
Pages (from-to)167-196
Number of pages30
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume40
Issue number2
DOIs
StatePublished - Mar 1 2004

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Keywords

  • Central limit theorem
  • Fluctuations from hydrodynamic limit
  • Gaussian random field

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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