Least Squares Estimation for α-Fractional Bridge with Discrete Observations
We consider a fractional bridge defined as dXt=-α(Xt/(T-t))dt+dBtH, 0≤t<T, where BH is a fractional Brownian motion of Hurst parameter H>1/2 and parameter α>0 is unknown. We are interested in the problem of estimating the unknown parameter α>0. Assume that the process is observed at dis...
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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/10.1155/2014/748376 |
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| _version_ | 1832555878033653760 |
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| author | Guangjun Shen Xiuwei Yin |
| author_facet | Guangjun Shen Xiuwei Yin |
| author_sort | Guangjun Shen |
| collection | DOAJ |
| description | We consider a fractional bridge defined as dXt=-α(Xt/(T-t))dt+dBtH, 0≤t<T, where BH is a fractional Brownian motion of Hurst parameter H>1/2 and parameter α>0 is unknown. We are interested in the problem of estimating the unknown parameter α>0. Assume that the process is observed at discrete time ti=iΔn, i=0,…,n, and Tn=nΔn denotes the length of the “observation window.” We construct a least squares estimator α^n of α which is consistent; namely, α^n converges to α in probability as n→∞. |
| format | Article |
| id | doaj-art-b71ab0f5a93547de949c469564336265 |
| 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-b71ab0f5a93547de949c4695643362652025-02-03T05:47:04ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/748376748376Least Squares Estimation for α-Fractional Bridge with Discrete ObservationsGuangjun Shen0Xiuwei Yin1Department of Mathematics, Anhui Normal University, Wuhu 241000, ChinaDepartment of Mathematics, Anhui Normal University, Wuhu 241000, ChinaWe consider a fractional bridge defined as dXt=-α(Xt/(T-t))dt+dBtH, 0≤t<T, where BH is a fractional Brownian motion of Hurst parameter H>1/2 and parameter α>0 is unknown. We are interested in the problem of estimating the unknown parameter α>0. Assume that the process is observed at discrete time ti=iΔn, i=0,…,n, and Tn=nΔn denotes the length of the “observation window.” We construct a least squares estimator α^n of α which is consistent; namely, α^n converges to α in probability as n→∞.http://dx.doi.org/10.1155/2014/748376 |
| spellingShingle | Guangjun Shen Xiuwei Yin Least Squares Estimation for α-Fractional Bridge with Discrete Observations Abstract and Applied Analysis |
| title | Least Squares Estimation for α-Fractional Bridge with Discrete Observations |
| title_full | Least Squares Estimation for α-Fractional Bridge with Discrete Observations |
| title_fullStr | Least Squares Estimation for α-Fractional Bridge with Discrete Observations |
| title_full_unstemmed | Least Squares Estimation for α-Fractional Bridge with Discrete Observations |
| title_short | Least Squares Estimation for α-Fractional Bridge with Discrete Observations |
| title_sort | least squares estimation for α fractional bridge with discrete observations |
| url | http://dx.doi.org/10.1155/2014/748376 |
| work_keys_str_mv | AT guangjunshen leastsquaresestimationforafractionalbridgewithdiscreteobservations AT xiuweiyin leastsquaresestimationforafractionalbridgewithdiscreteobservations |