Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion
Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. Karhunen-Loève expansion for this process is obtained together with t...
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| Main Authors: | , , , |
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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/10.1155/2014/457051 |
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| _version_ | 1832556656219652096 |
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| author | Yongchun Zhou Xiaohui Ai Minghao Lv Boping Tian |
| author_facet | Yongchun Zhou Xiaohui Ai Minghao Lv Boping Tian |
| author_sort | Yongchun Zhou |
| collection | DOAJ |
| description | Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. Karhunen-Loève expansion for this process is obtained together with the relationship of that of a generalized Brownian bridge. As applications, Laplace transform, large deviation, and small deviation are given. |
| format | Article |
| id | doaj-art-076df4fb7f1e4e6081bca8e65782f6a7 |
| 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-076df4fb7f1e4e6081bca8e65782f6a72025-02-03T05:44:39ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/457051457051Karhunen-Loève Expansion for the Second Order Detrended Brownian MotionYongchun Zhou0Xiaohui Ai1Minghao Lv2Boping Tian3Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaBased on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. Karhunen-Loève expansion for this process is obtained together with the relationship of that of a generalized Brownian bridge. As applications, Laplace transform, large deviation, and small deviation are given.http://dx.doi.org/10.1155/2014/457051 |
| spellingShingle | Yongchun Zhou Xiaohui Ai Minghao Lv Boping Tian Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion Abstract and Applied Analysis |
| title | Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion |
| title_full | Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion |
| title_fullStr | Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion |
| title_full_unstemmed | Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion |
| title_short | Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion |
| title_sort | karhunen loeve expansion for the second order detrended brownian motion |
| url | http://dx.doi.org/10.1155/2014/457051 |
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