On the paper weak convergence of some classes of martingales with jumps
成果类型：
Article
署名作者：
Nishiyama, Yoichi
署名单位：
Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117906000000755
发表日期：
2007
页码：
1194-1200
关键词：
摘要：
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 modem theory of empirical processes.
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