Parameter Estimation for Fractional Diffusion Process with Discrete Observations
This paper deals with the problem of estimating the parameters for fractional diffusion process from discrete observations when the Hurst parameter H is unknown. With combination of several methods, such as the Donsker type approximate formula of fractional Brownian motion, quadratic variation metho...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/9036285 |
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| _version_ | 1849308651676762112 |
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| author | Yuxia Su Yutian Wang |
| author_facet | Yuxia Su Yutian Wang |
| author_sort | Yuxia Su |
| collection | DOAJ |
| description | This paper deals with the problem of estimating the parameters for fractional diffusion process from discrete observations when the Hurst parameter H is unknown. With combination of several methods, such as the Donsker type approximate formula of fractional Brownian motion, quadratic variation method, and the maximum likelihood approach, we give the parameter estimations of the Hurst index, diffusion coefficients, and volatility and then prove their strong consistency. Finally, an extension for generalized fractional diffusion process and further work are briefly discussed. |
| format | Article |
| id | doaj-art-0ea6ebdc090f4bc9a043533c4b8c4296 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-0ea6ebdc090f4bc9a043533c4b8c42962025-08-20T03:54:24ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/90362859036285Parameter Estimation for Fractional Diffusion Process with Discrete ObservationsYuxia Su0Yutian Wang1School of Statistics, Qufu Normal University, Jining, Shandong 273165, ChinaSchool of Software Engineering, Qufu Normal University, Jining, Shandong 273165, ChinaThis paper deals with the problem of estimating the parameters for fractional diffusion process from discrete observations when the Hurst parameter H is unknown. With combination of several methods, such as the Donsker type approximate formula of fractional Brownian motion, quadratic variation method, and the maximum likelihood approach, we give the parameter estimations of the Hurst index, diffusion coefficients, and volatility and then prove their strong consistency. Finally, an extension for generalized fractional diffusion process and further work are briefly discussed.http://dx.doi.org/10.1155/2019/9036285 |
| spellingShingle | Yuxia Su Yutian Wang Parameter Estimation for Fractional Diffusion Process with Discrete Observations Journal of Function Spaces |
| title | Parameter Estimation for Fractional Diffusion Process with Discrete Observations |
| title_full | Parameter Estimation for Fractional Diffusion Process with Discrete Observations |
| title_fullStr | Parameter Estimation for Fractional Diffusion Process with Discrete Observations |
| title_full_unstemmed | Parameter Estimation for Fractional Diffusion Process with Discrete Observations |
| title_short | Parameter Estimation for Fractional Diffusion Process with Discrete Observations |
| title_sort | parameter estimation for fractional diffusion process with discrete observations |
| url | http://dx.doi.org/10.1155/2019/9036285 |
| work_keys_str_mv | AT yuxiasu parameterestimationforfractionaldiffusionprocesswithdiscreteobservations AT yutianwang parameterestimationforfractionaldiffusionprocesswithdiscreteobservations |