This paper deals with weak convergence of stochastic integrals with
respect to multivariate point processes. The results are given in terms of an
entropy condition for partitioning of the index set of the integrands, which is
a sort of $L^2$-bracketing.We also consider $\ell^\infty$-valued martingale
difference arrays, and present natural generalizations of
Jain–Marcus’s and Ossiander’s central limit theorems. As
an application,the asymptotic behavior of log-likelihood ratio random fields in
general statistical experiments with abstract parameters is derived.
Publié le : 2000-04-14
Classification:
Weak convergence,
central limit theorem,
point process,
martingale,
likelihood,
Markov chain.,
60F05,
60F17,
62F20
@article{1019160257,
author = {Nishiyama, Yoichi},
title = {Weak convergence of some classes of martingales with jumps},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 685-712},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160257}
}
Nishiyama, Yoichi. Weak convergence of some classes of martingales with jumps. Ann. Probab., Tome 28 (2000) no. 1, pp. 685-712. http://gdmltest.u-ga.fr/item/1019160257/