An infinite dimensional central limit theorem for correlated martingales

  • Grigorescu I
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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. © 2003 Elsevier SAS. All rights reserved.

Author-supplied keywords

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

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  • Ilie Grigorescu

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