Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus
We study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1)(Si+1H2-SiH2), as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in term...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/635917 |
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| author | Yuquan Cang Junfeng Liu Yan Zhang |
| author_facet | Yuquan Cang Junfeng Liu Yan Zhang |
| author_sort | Yuquan Cang |
| collection | DOAJ |
| description | We study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1)(Si+1H2-SiH2), as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion. |
| format | Article |
| id | doaj-art-58d16167542a4a93bf1a665da0627d40 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-58d16167542a4a93bf1a665da0627d402025-02-03T01:22:29ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/635917635917Nonparametric Regression with Subfractional Brownian Motion via Malliavin CalculusYuquan Cang0Junfeng Liu1Yan Zhang2School of Mathematics and Statistics, Nanjing Audit University, 86 West Yushan Road, Pukou, Nanjing 211815, ChinaSchool of Mathematics and Statistics, Nanjing Audit University, 86 West Yushan Road, Pukou, Nanjing 211815, ChinaSchool of Mathematics and Statistics, Nanjing Audit University, 86 West Yushan Road, Pukou, Nanjing 211815, ChinaWe study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1)(Si+1H2-SiH2), as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.http://dx.doi.org/10.1155/2014/635917 |
| spellingShingle | Yuquan Cang Junfeng Liu Yan Zhang Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus Abstract and Applied Analysis |
| title | Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus |
| title_full | Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus |
| title_fullStr | Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus |
| title_full_unstemmed | Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus |
| title_short | Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus |
| title_sort | nonparametric regression with subfractional brownian motion via malliavin calculus |
| url | http://dx.doi.org/10.1155/2014/635917 |
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