Asymptotic behavior for bi-fractional regression models via Malliavin calculus
Asymptotic behavior for bi-fractional regression models via Malliavin calculus
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DOI：
10.1007/s11464-013-0312-z
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发表时间：
2014-02
影响因子：
--
通讯作者：
Guangjun Shen;Litan Yan
中科院分区：
文献类型：
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作者：
Guangjun Shen;Litan Yan
假设有两个独立的双分数布朗运动。本文作为分数阶回归模型的自然推广，考虑了序列$$S_n : = \sum\limits_{i = 0}^{n - 1} {K\left( {n^\alpha B_i^{H_1 ,K_1 } } \right)\left( {B_{i + 1}^{H_2 ,K_2 } - B_i^{H_2 ,K_2 } } \right),}$$的渐近性质，其中kis为标准高斯核函数，带宽参数α满足若干假设。我们证明了它的极限分布是一个涉及双分数阶布朗运动局部时间的混合正态律。并利用马立文演算的方法给出了序列的稳定收敛性。
Letandbe 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 $$S_n : = \sum\limits_{i = 0}^{n - 1} {K\left( {n^\alpha B_i^{H_1 ,K_1 } } \right)\left( {B_{i + 1}^{H_2 ,K_2 } - B_i^{H_2 ,K_2 } } \right),}$$ whereKis a standard Gaussian kernel function and the bandwidth parameterαsatisfies certain hypotheses. We show that its limiting distribution is a mixed normal law involving the local time of the bi-fractional Brownian motion. We also give the stable convergence of the sequenceSnby using the techniques of the Malliavin calculus.