Weak convergence of some classes of martingales with jumps

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Abstract

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 L2-bracketing. We also consider lα-valued martingale difference arrays, and present natural generalizations of Jain-Marcus's and Ossian-der'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.

Original languageEnglish
Pages (from-to)685-712
Number of pages28
JournalAnnals of Probability
Volume28
Issue number2
DOIs
Publication statusPublished - 2000 Apr

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Keywords

  • Central limit theorem
  • Likelihood
  • Markov chain
  • Martingale
  • Point process
  • Weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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