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arXiv · 2406.07889

Nonparametric estimation of linear multiplier for processes driven by a bifractional Brownian motion

B. L. S. Prakasa Rao
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Abstract

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 $ε\rightarrow 0.$

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B. L. S. Prakasa Rao. 2024-06-12. Nonparametric estimation of linear multiplier for processes driven by a bifractional Brownian motion. https://arxiv.org/abs/2406.07889

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