Weak convergence of some classes of martingales with jumps

Research output: Contribution to journalArticle

15 Citations (Scopus)

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
Publication statusPublished - 2000 Apr
Externally publishedYes

Fingerprint

Martingale Difference
Entropy Condition
Log-likelihood Ratio
Stochastic Integral
Point Process
Integrand
Weak Convergence
Martingale
Central limit theorem
Random Field
Sort
Partitioning
Jump
Asymptotic Behavior
Experiment
Generalization
Class
Integral
Likelihood ratio
Asymptotic behavior

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Weak convergence of some classes of martingales with jumps. / Nishiyama, Yoichi.

In: Annals of Probability, Vol. 28, No. 2, 04.2000, p. 685-712.

Research output: Contribution to journalArticle

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