Nonparametric estimation of linear multiplier for processes driven by a Hermite process
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910025648177152 |
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| author | Rao, B. L. S. Prakasa |
| author_facet | Rao, B. L. S. Prakasa |
| contents | We study the problem of nonparametric estimation of the linear multiplier function $θ(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=θ(t) X_tdt+ εdZ^{q,H}_t, X_0=x_0, 0\leq t \leq T$$ where $\{Z^{q,H}_t, t \geq 0\}$ is a Hermite process with known order $q$ and known self-similarity parameter $H \in (\frac{1}{2},1).$ We investigate the asymptotic behaviour of the estimator of the unknown function $θ(t)$ as $ε\rightarrow 0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonparametric estimation of linear multiplier for processes driven by a Hermite process Rao, B. L. S. Prakasa Statistics Theory Probability 60G18 We study the problem of nonparametric estimation of the linear multiplier function $θ(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=θ(t) X_tdt+ εdZ^{q,H}_t, X_0=x_0, 0\leq t \leq T$$ where $\{Z^{q,H}_t, t \geq 0\}$ is a Hermite process with known order $q$ and known self-similarity parameter $H \in (\frac{1}{2},1).$ We investigate the asymptotic behaviour of the estimator of the unknown function $θ(t)$ as $ε\rightarrow 0.$ |
| title | Nonparametric estimation of linear multiplier for processes driven by a Hermite process |
| topic | Statistics Theory Probability 60G18 |
| url | https://arxiv.org/abs/2602.16223 |