This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685–712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the parameter space is satisfied, then the tightness follows. Our approach is based on the entropy techniques developed in the modern theory of empirical processes.
Publié le : 2007-05-14
Classification:
Maximal inequality,
weak convergence,
martingale,
integer-valued random measure,
entropy,
60F05,
60F17
@article{1178804327,
author = {Nishiyama, Yoichi},
title = {On the paper ``Weak convergence of some classes of martingales with jumps''},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 1194-1200},
language = {en},
url = {http://dml.mathdoc.fr/item/1178804327}
}
Nishiyama, Yoichi. On the paper “Weak convergence of some classes of martingales with jumps”. Ann. Probab., Tome 35 (2007) no. 1, pp. 1194-1200. http://gdmltest.u-ga.fr/item/1178804327/