Drift estimation for rough processes under small noise asymptotic : trajectory fitting method
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913146821672960 |
|---|---|
| author | Gloter, Arnaud Yoshida, Nakahiro |
| author_facet | Gloter, Arnaud Yoshida, Nakahiro |
| contents | We consider a process $X^\ve$ that solves a stochastic Volterra equation with an unknown parameter $θ^\star$ in the drift function. The Volterra kernel is singular, and includes as an example, $K\_0(u)=c u^{α-1/2} \id{u>0}$ with $α\in (0,1/2)$. It is assumed that the diffusion coefficient is proportional to $\ve \to 0$. From an observation of the path $(X^\ve\_s)\_{s\in[0,T]}$, we construct a Trajectory Fitting Estimator, which is shown to be consistent and asymptotically normal. We also specify identifiability conditions insuring the $L^p$ convergence of the estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Drift estimation for rough processes under small noise asymptotic : trajectory fitting method Gloter, Arnaud Yoshida, Nakahiro Statistics Theory We consider a process $X^\ve$ that solves a stochastic Volterra equation with an unknown parameter $θ^\star$ in the drift function. The Volterra kernel is singular, and includes as an example, $K\_0(u)=c u^{α-1/2} \id{u>0}$ with $α\in (0,1/2)$. It is assumed that the diffusion coefficient is proportional to $\ve \to 0$. From an observation of the path $(X^\ve\_s)\_{s\in[0,T]}$, we construct a Trajectory Fitting Estimator, which is shown to be consistent and asymptotically normal. We also specify identifiability conditions insuring the $L^p$ convergence of the estimator. |
| title | Drift estimation for rough processes under small noise asymptotic : trajectory fitting method |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2503.03347 |