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Asymptotic behavior for bi-fractional regression models via Malliavin calculus
  • ISSN号：1673-3452
  • 期刊名称：Frontiers of Mathematics in China
  • 时间：2014
  • 页码：151-179
  • 分类：O212.1[理学—概率论与数理统计;理学—数学] O121.5[理学—数学;理学—基础数学]
  • 作者机构：[1]Department of Mathematics, Anhui Normal University, Wuhu 241000, China, [2]Department of Mathematics, Donghua University, Shanghai 201620, China
  • 相关基金：Acknowledgements The authors would like to thank the anonymous referees whose remarks and suggestions greatly improved the presentation of the paper. Guangjun Shen was supported in part by the National Natural Science Foundation of China （Grant No. 11271020） and the Natural Science Foundation of Anhui Province （1208085MA11）. Litan YAN was partially supported by the National Natural Science Foundation of China （Grant No. 11171062） and the Innovation Program of Shanghai Municipal Education Commission （12ZZ063）.
  • 相关项目：G-分数布朗运动与Hermite过程的分析及其相关问题
作者： 申广君（研究生)|闫理坦|
关键词： 回归模型, 小数, 分形布朗运动, 演算, 高斯核函数, 渐近行为, 极限分布, 稳定收敛, Bi-fractional Brownian motion （bi-fBm）, Malliavin calculus, regression model
中文摘要：

让 $B ^{ H_1， K_1 }$ 并且 $B ^{ H_2， K_2 }$ 是二个独立双性人部分的 Brownian 运动。在这份报纸，作为对部分回归模型的自然扩展，我们考虑顺序 $$S_n 的 asymptotic 行为：=\sum\limits_{ i = 0 }^{ n - 1 }{ K\left ({ n ^ \alpha B_i ^{ H_1 ， K_1 }} \right ) \left ({B_{ i + 1 }^{ H_2 ， K_2 }- B_i ^{ H_2 ， K_2 }} \right )，} K 是一个标准 Gaussian 内核函数的$$和带宽参数满足某些假设。我们证明它的限制分发是包含双性人部分的 Brownian 运动 $B ^ 的本地时间的一条混合正常法律 { H_1， K_1 }$ 。我们也由使用 Malliavin 演算的技术给顺序 S n 的稳定的集中。

英文摘要：

Let B^H1,K1 and BH2,K2 be two independent bi-fractional Brownian motions. In this paper, as a natural extension to the fractional regression model, we consider the asymptotic behavior of the sequence Sn：=∑i=0^n-1K（n^αBi^H,K1）（Bi＋1^H2,K2-Bi^H2,K2）where K is a standard Gaussian kernel function and the bandwidth parameter α satisfies certain hypotheses. We show that its limiting distribution is a mixed normal law involving the local time of the bi-fractional Brownian motion B^H1,K1. We also give the stable convergence of the sequence Sn by using the techniques of the Malliavin calculus.

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分数布朗运动的扩张及其随机分析
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期刊信息
  • 《中国数学前沿：英文版》
  • 主管单位:中华人民共和国教育部
  • 主办单位:高等教育出版社
  • 主编：张恭庆
  • 地址：北京市朝阳区惠新东街4号富盛大厦15层
  • 邮编：100029
  • 邮箱：
  • 电话：010-58556485
  • 国际标准刊号：ISSN：1673-3452
  • 国内统一刊号：ISSN：11-5739/O1
  • 邮发代号:80-964
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国剑桥科学文摘,美国科学引文索引（扩展库）
  • 被引量:10