### 抄録

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.

元の言語 | English |
---|---|

ページ（範囲） | 685-712 |

ページ数 | 28 |

ジャーナル | Annals of Probability |

巻 | 28 |

発行部数 | 2 |

出版物ステータス | Published - 2000 4 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### これを引用

*Annals of Probability*,

*28*(2), 685-712.

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

研究成果: Article

*Annals of Probability*, 巻. 28, 番号 2, pp. 685-712.

}

TY - JOUR

T1 - Weak convergence of some classes of martingales with jumps

AU - Nishiyama, Yoichi

PY - 2000/4

Y1 - 2000/4

N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Likelihood

KW - Markov chain

KW - Martingale

KW - Point process

KW - Weak convergence

UR - http://www.scopus.com/inward/record.url?scp=0034345594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034345594&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034345594

VL - 28

SP - 685

EP - 712

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 2

ER -