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.
CITATION STYLE
Grigorescu, I. (2004). An infinite dimensional central limit theorem for correlated martingales. Annales de l’institut Henri Poincare (B) Probability and Statistics, 40(2), 167–196. https://doi.org/10.1016/j.anihpb.2003.03.001
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