Some central limit theorems for ℓ-valued semimartingales and their applications

研究成果: Article査読

10 被引用数 (Scopus)

抄録

This paper is devoted to the generalization of central limit theorems for empirical processes to several types of ℓ(Ψ)-valued continuous-time stochastic processes t /\/\/\> Xnt = (Xn,ψt|ψ ∈ Ψ) where Ψ is a non-empty set. We deal with three kinds of situations as follows. Each coordinate process t /\/\/\> Xn,ψt is: (i) a general semimartingale; (ii) a stochastic integral of a predictable function with respect to an integer-valued random measure; (iii) a continuous local martingale. Some applications to statistical inference problems are also presented. We prove the functional asymptotic normality of generalized Nelson-Aalen's estimator in the multiplicative intensity model for marked point processes. Its asymptotic efficiency in the sense of convolution theorem is also shown. The asymptotic behavior of log-likelihood ratio random fields of certain continuous semimartingales is derived.

本文言語English
ページ(範囲)459-494
ページ数36
ジャーナルProbability Theory and Related Fields
108
4
DOI
出版ステータスPublished - 1997 8
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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