Nonparametric estimation of linear multiplier for processes driven by a bifractional Brownian motion
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917691566063616 |
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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 $$dX_t=θ(t)X_tdt+εdW_t^{H,K}, X_0=x_0,0\leq t \leq T$$ where $\{W_t^{H,K}, t \geq 0\}$ is a bifractional Brownian motion with known parameters $H\in (0,1), K\in (0,1]$ and $HK\in (\frac{1}{2},1).$ We investigate the asymptotic behaviour of the estimator of the unknown function $θ(t)$ as $ε\rightarrow 0.$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_07889 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonparametric estimation of linear multiplier for processes driven by a bifractional Brownian motion Rao, B. L. S. Prakasa Statistics Theory 60G22 We study the problem of nonparametric estimation of the linear multiplier function $θ(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=θ(t)X_tdt+εdW_t^{H,K}, X_0=x_0,0\leq t \leq T$$ where $\{W_t^{H,K}, t \geq 0\}$ is a bifractional Brownian motion with known parameters $H\in (0,1), K\in (0,1]$ and $HK\in (\frac{1}{2},1).$ 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 bifractional Brownian motion |
| topic | Statistics Theory 60G22 |
| url | https://arxiv.org/abs/2406.07889 |