2007/07/31 by Yoichi Nishiyama · 1 citation
Mathematics · #math.PR #msc:60F05 #msc:60F17
paper · pdf · doi:10.1214/009117906000000755
published as Annals of Probability 2007, Vol. 35, No. 3, 1194-1200 · Published at http://dx.doi.org/10.1214/009117906000000755 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2007/07/31 · arxiv updated 2011/11/09
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.