Nonparametric regression with subfractional Brownian motion via Malliavin calculus
type: Item
instance of: scholarly article
title: Nonparametric regression with subfractional Brownian motion via Malliavin calculus
zbMATH Open document ID: 1474.62119
DOI: 10.1155/2014/635917
author: Yuquan Cang
author: Yan Zhang
author: Junfeng Liu
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We study the asymptotic behavior of the sequence \(S_n = \sum_{i = 0}^{n - 1} K(n^\alpha S_i^{H_1})(S_{i + 1}^{H_2} - S_i^{H_2})\), as \(n\) tends to infinity, where \(S^{H_1}\) and \(S^{H_2}\) are two independent subfractional Brownian motions with indices \(H_1\) and \(H_2\), respectively. \(K\) is a kernel function and the bandwidth parameter \(\alpha\) satisfies some hypotheses in terms of \(H_1\) and \(H_2\). Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion \(S^{H_1}\). We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60G22
zbMATH DE Number: 7022793
Wikidata QID: Q59040247
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/635917
OpenAlex ID: W1997356760
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description: scientific article; zbMATH DE number 7022793