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 language | English (US) |
---|---|
Pages (from-to) | 167-196 |
Number of pages | 30 |
Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
Volume | 40 |
Issue number | 2 |
DOIs | |
State | Published - Mar 2004 |
Keywords
- Central limit theorem
- Fluctuations from hydrodynamic limit
- Gaussian random field
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty