On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910841281970176 |
|---|---|
| author | Marie, Nicolas |
| author_facet | Marie, Nicolas |
| contents | This paper deals with a Skorokhod's integral based least squares type estimator $\widehatθ_N$ of the drift parameter $θ_0$ computed from $N\in\mathbb N^*$ (possibly dependent) copies $X^1,\dots,X^N$ of the solution $X$ of $dX_t =θ_0b(X_t)dt +σdB_t$, where $B$ is a fractional Brownian motion of Hurst index $H\in (1/3,1)$. On the one hand, some convergence results are established on $\widehatθ_N$ when $H = 1/2$. On the other hand, when $H\neq 1/2$, Skorokhod's integral based estimators as $\widehatθ_N$ cannot be computed from data, but in this paper some convergence results are established on a computable approximation of $\widehatθ_N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05341 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE Marie, Nicolas Statistics Theory Probability This paper deals with a Skorokhod's integral based least squares type estimator $\widehatθ_N$ of the drift parameter $θ_0$ computed from $N\in\mathbb N^*$ (possibly dependent) copies $X^1,\dots,X^N$ of the solution $X$ of $dX_t =θ_0b(X_t)dt +σdB_t$, where $B$ is a fractional Brownian motion of Hurst index $H\in (1/3,1)$. On the one hand, some convergence results are established on $\widehatθ_N$ when $H = 1/2$. On the other hand, when $H\neq 1/2$, Skorokhod's integral based estimators as $\widehatθ_N$ cannot be computed from data, but in this paper some convergence results are established on a computable approximation of $\widehatθ_N$. |
| title | On a Computable Skorokhod's Integral Based Estimator of the Drift Parameter in Fractional SDE |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2301.05341 |