An infinite dimensional central limit theorem for correlated martingales

Ilie Grigorescu

doi:10.1016/j.anihpb.2003.03.001

An infinite dimensional central limit theorem for correlated martingales

Ilie Grigorescu

Mathematics

Research output: Contribution to journal › Article

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	https://doi.org/10.1016/j.anihpb.2003.03.001
State	Published - Mar 2004

Fingerprint

Martingale

Central limit theorem

Density Theorem

Functional Central Limit Theorem

Gaussian Random Field

Spaces of Continuous Functions

Empirical Distribution

Weak Convergence

Explicit Formula

Trajectory

Class

Empirical distribution

Weak convergence

Random field

Keywords

Central limit theorem
Fluctuations from hydrodynamic limit
Gaussian random field

ASJC Scopus subject areas

Statistics and Probability

Cite this

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

An infinite dimensional central limit theorem for correlated martingales. / Grigorescu, Ilie.

In: Annales de l'institut Henri Poincare (B) Probability and Statistics, Vol. 40, No. 2, 03.2004, p. 167-196.

Research output: Contribution to journal › Article

Grigorescu, I 2004, 'An infinite dimensional central limit theorem for correlated martingales', Annales de l'institut Henri Poincare (B) Probability and Statistics, vol. 40, no. 2, pp. 167-196. https://doi.org/10.1016/j.anihpb.2003.03.001

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

Grigorescu, Ilie. / An infinite dimensional central limit theorem for correlated martingales. In: Annales de l'institut Henri Poincare (B) Probability and Statistics. 2004 ; Vol. 40, No. 2. pp. 167-196.

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Access to Document

10.1016/j.anihpb.2003.03.001