Parameter estimation in mixed fractional stochastic heat equation
The paper is devoted to a stochastic heat equation with a mixed fractional Brownian noise. We investigate the covariance structure, stationarity, upper bounds and asymptotic behavior of the solution. Based on its discrete-time observations, we construct a strongly consistent estimator for the Hurst...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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VTeX
2023-01-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/23-VMSTA221 |
| _version_ | 1827974096268296192 |
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| author | Diana Avetisian Kostiantyn Ralchenko |
| author_facet | Diana Avetisian Kostiantyn Ralchenko |
| author_sort | Diana Avetisian |
| collection | DOAJ |
| description | The paper is devoted to a stochastic heat equation with a mixed fractional Brownian noise. We investigate the covariance structure, stationarity, upper bounds and asymptotic behavior of the solution. Based on its discrete-time observations, we construct a strongly consistent estimator for the Hurst index H and prove the asymptotic normality for $H. Then assuming the parameter H to be known, we deal with joint estimation of the coefficients at the Wiener process and at the fractional Brownian motion. The quality of estimators is illustrated by simulation experiments. |
| first_indexed | 2024-04-09T19:48:16Z |
| format | Article |
| id | doaj.art-0521d7360a0f45dfb646de7596d665ff |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-04-09T19:48:16Z |
| publishDate | 2023-01-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-0521d7360a0f45dfb646de7596d665ff2023-04-03T11:01:08ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542023-01-0110217519510.15559/23-VMSTA221Parameter estimation in mixed fractional stochastic heat equationDiana Avetisian0Kostiantyn Ralchenko1Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601 Kyiv, UkraineDepartment of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, 01601 Kyiv, Ukraine; Sydney Mathematical Research Institute, The University of Sydney, Sydney NSW 2006, AustraliaThe paper is devoted to a stochastic heat equation with a mixed fractional Brownian noise. We investigate the covariance structure, stationarity, upper bounds and asymptotic behavior of the solution. Based on its discrete-time observations, we construct a strongly consistent estimator for the Hurst index H and prove the asymptotic normality for $H. Then assuming the parameter H to be known, we deal with joint estimation of the coefficients at the Wiener process and at the fractional Brownian motion. The quality of estimators is illustrated by simulation experiments.https://www.vmsta.org/doi/10.15559/23-VMSTA221Stochastic partial differential equationmixed fractional Brownian motionHurst index estimationstrong consistencyAsymptotic normality |
| spellingShingle | Diana Avetisian Kostiantyn Ralchenko Parameter estimation in mixed fractional stochastic heat equation Modern Stochastics: Theory and Applications Stochastic partial differential equation mixed fractional Brownian motion Hurst index estimation strong consistency Asymptotic normality |
| title | Parameter estimation in mixed fractional stochastic heat equation |
| title_full | Parameter estimation in mixed fractional stochastic heat equation |
| title_fullStr | Parameter estimation in mixed fractional stochastic heat equation |
| title_full_unstemmed | Parameter estimation in mixed fractional stochastic heat equation |
| title_short | Parameter estimation in mixed fractional stochastic heat equation |
| title_sort | parameter estimation in mixed fractional stochastic heat equation |
| topic | Stochastic partial differential equation mixed fractional Brownian motion Hurst index estimation strong consistency Asymptotic normality |
| url | https://www.vmsta.org/doi/10.15559/23-VMSTA221 |
| work_keys_str_mv | AT dianaavetisian parameterestimationinmixedfractionalstochasticheatequation AT kostiantynralchenko parameterestimationinmixedfractionalstochasticheatequation |