On interpolation problem for multidimensional harmonizable stable sequences with noise observations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910840352931840 |
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| author | Moklyachuk, Mikhail |
| author_facet | Moklyachuk, Mikhail |
| contents | We consider the problem of optimal linear estimation of the functional $$A_N \vecξ =\sum_{j = 0}^{N} (\vec{a}(j))^{\top} \vecξ(j)$$ that depends on the unknown values $\vecξ(j),j=0,1,\dots,N,$ of a vector-valued harmonizable symmetric $α$-stable random sequence $\vecξ(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$, from observations of the sequence $\vecξ(j)+\vecη(j)$ at points $j\in\mathbb Z\setminus\{0,1,\dots,N\}$. We consider the problem for mutually independent vector-valued harmonizable symmetric $α$-stable random sequences $\vecξ(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$ and $\vecη(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$ which have absolutely continuous spectral measures and the spectral densities $f(θ)$ and $g(θ)$ satisfying the minimality condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On interpolation problem for multidimensional harmonizable stable sequences with noise observations Moklyachuk, Mikhail Statistics Theory Primary: 60G10, 60G25, 60G35, Secondary: 62M20, 93E10, 93E11 We consider the problem of optimal linear estimation of the functional $$A_N \vecξ =\sum_{j = 0}^{N} (\vec{a}(j))^{\top} \vecξ(j)$$ that depends on the unknown values $\vecξ(j),j=0,1,\dots,N,$ of a vector-valued harmonizable symmetric $α$-stable random sequence $\vecξ(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$, from observations of the sequence $\vecξ(j)+\vecη(j)$ at points $j\in\mathbb Z\setminus\{0,1,\dots,N\}$. We consider the problem for mutually independent vector-valued harmonizable symmetric $α$-stable random sequences $\vecξ(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$ and $\vecη(j)=\left \{ ξ_ {k} (j) \right \}_{k = 1} ^ {T}$ which have absolutely continuous spectral measures and the spectral densities $f(θ)$ and $g(θ)$ satisfying the minimality condition. |
| title | On interpolation problem for multidimensional harmonizable stable sequences with noise observations |
| topic | Statistics Theory Primary: 60G10, 60G25, 60G35, Secondary: 62M20, 93E10, 93E11 |
| url | https://arxiv.org/abs/2502.15717 |