Parameter estimation for fractional stochastic heat equations : Berry-Esséen bounds in CLTs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910595440181248 |
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| author | Douissi, Soukaina Alshahrani, Fatimah |
| author_facet | Douissi, Soukaina Alshahrani, Fatimah |
| contents | The aim of this work is to estimate the drift coefficient of a fractional heat equation driven by an additive space-time noise using the Maximum likelihood estimator (MLE). In the first part of the paper, the first $N$ Fourier modes of the solution are observed continuously over a finite time interval $[0, T ]$. The explicit upper bounds for the Wasserstein distance for the central limit theorem of the MLE is provided when $N \rightarrow \infty$ and/or $T \rightarrow \infty$. While in the second part of the paper, the $N$ Fourier modes are observed at uniform time grid : $t_i = i \frac{T}{M}$, $i=0,..,M,$ where $M$ is the number of time grid points. The consistency and asymptotic normality are studied when $T,M,N \rightarrow + \infty$ in addition to the rate of convergence in law in the CLT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameter estimation for fractional stochastic heat equations : Berry-Esséen bounds in CLTs Douissi, Soukaina Alshahrani, Fatimah Statistics Theory Probability The aim of this work is to estimate the drift coefficient of a fractional heat equation driven by an additive space-time noise using the Maximum likelihood estimator (MLE). In the first part of the paper, the first $N$ Fourier modes of the solution are observed continuously over a finite time interval $[0, T ]$. The explicit upper bounds for the Wasserstein distance for the central limit theorem of the MLE is provided when $N \rightarrow \infty$ and/or $T \rightarrow \infty$. While in the second part of the paper, the $N$ Fourier modes are observed at uniform time grid : $t_i = i \frac{T}{M}$, $i=0,..,M,$ where $M$ is the number of time grid points. The consistency and asymptotic normality are studied when $T,M,N \rightarrow + \infty$ in addition to the rate of convergence in law in the CLT. |
| title | Parameter estimation for fractional stochastic heat equations : Berry-Esséen bounds in CLTs |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2409.05416 |