Exact convergence rates to derivatives of local time for some self-similar Gaussian processes
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914861252870144 |
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| author | Hong, Minhao |
| author_facet | Hong, Minhao |
| contents | In this article, for some $d-$dimensional Gaussian processes
\[X=\big\{X_t=(X^1_t,\cdots,X^d_t):t\ge0\big\},\]
whose components are i.i.d. $1-$dimensional self-similar Gaussian process with Hurst index $H\in(0,1)$, we consider the asymptotic behavior of approximation of its $\boldsymbol{k}-$th derivatives of local time under certain mild conditions, where
$\boldsymbol{k}=(k_1,\cdots,k_d)$ and $k_\ell$'s are non-negative real numbers. We will give a derivative version of the limit theorems for functional of Gaussian processes and use this result to get the asymptotic behaviors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact convergence rates to derivatives of local time for some self-similar Gaussian processes Hong, Minhao Probability In this article, for some $d-$dimensional Gaussian processes \[X=\big\{X_t=(X^1_t,\cdots,X^d_t):t\ge0\big\},\] whose components are i.i.d. $1-$dimensional self-similar Gaussian process with Hurst index $H\in(0,1)$, we consider the asymptotic behavior of approximation of its $\boldsymbol{k}-$th derivatives of local time under certain mild conditions, where $\boldsymbol{k}=(k_1,\cdots,k_d)$ and $k_\ell$'s are non-negative real numbers. We will give a derivative version of the limit theorems for functional of Gaussian processes and use this result to get the asymptotic behaviors. |
| title | Exact convergence rates to derivatives of local time for some self-similar Gaussian processes |
| topic | Probability |
| url | https://arxiv.org/abs/2407.05514 |