## 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 /\/\/\> X^{n}_{t} = (X^{n,ψ}_{t}|ψ ∈ Ψ) where Ψ is a non-empty set. We deal with three kinds of situations as follows. Each coordinate process t /\/\/\> X^{n,ψ}_{t} 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 |
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ページ（範囲） | 459-494 |

ページ数 | 36 |

ジャーナル | Probability Theory and Related Fields |

巻 | 108 |

号 | 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