Weak convergence of some classes of martingales with jumps

• 成果类型: Article
• 署名作者: Nishiyama, Y
• 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/aop/1019160257
• 发表日期: 2000
• 页码: 685-712
• 关键词: CENTRAL LIMIT-THEOREMS

摘要

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 l(infinity)-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.