Asymptotic behavior for bi-fractional regression models via Malliavin calculus

doi:10.1007/s11464-013-0312-z

Front Math Chin

2014, Vol. 9

Issue (1) : 151-179 https://doi.org/10.1007/s11464-013-0312-z

RESEARCH ARTICLE

Asymptotic behavior for bi-fractional regression models via Malliavin calculus

Guangjun SHEN¹, Litan YAN²(

)

1. Department of Mathematics, Anhui Normal University, Wuhu 241000, China; 2. Department of Mathematics, Donghua University, Shanghai 201620, China

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Abstract

Let B^H1,K1 and B^H2,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 sequenceSn:=∑i=0n-1K(nαBiH1,K1)(Bi+1H2,K2-BiH2,K2),where K is a standard Gaussian kernel function and the bandwidth parameter αsatisfies 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 S_n by using the techniques of the Malliavin calculus.

Keywords Bi-fractional Brownian motion (bi-fBm) Malliavin calculus regression model

Corresponding Author(s): YAN Litan,Email:litanyan@dhu.edu.cn

Issue Date: 01 February 2014

Cite this article:

Guangjun SHEN,Litan YAN. Asymptotic behavior for bi-fractional regression models via Malliavin calculus[J]. Front Math Chin, 2014, 9(1): 151-179.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-013-0312-z
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I1/151

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