Exact convergence rates in the central limit theorem for a class of martingales

Machkouri, M. El; Ouchti, L.

Bernoulli, Tome 13 (2007) no. 1, p. 981-999 / Harvested from Project Euclid

Résumé

We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and, for stationary sequences, the rate n^−1/2log n is reached.

Publié le : 2007-11-14
Classification: central limit theorem, Lindeberg’s decomposition, martingale difference sequence, rate of convergence

@article{1194625599,
     author = {Machkouri, M. El and Ouchti, L.},
     title = {Exact convergence rates in the central limit theorem for a class of martingales},
     journal = {Bernoulli},
     volume = {13},
     number = {1},
     year = {2007},
     pages = { 981-999},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1194625599}
}

Machkouri, M. El; Ouchti, L. Exact convergence rates in the central limit theorem for a class of martingales. Bernoulli, Tome 13 (2007) no. 1, pp.  981-999. http://gdmltest.u-ga.fr/item/1194625599/