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arXiv · 2602.16223

Nonparametric estimation of linear multiplier for processes driven by a Hermite process

B. L. S. Prakasa Rao
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Abstract

We study the problem of nonparametric estimation of the linear multiplier function $\theta(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=\theta(t) X_tdt+ \epsilon dZ^{q,H}_t, X_0=x_0, 0\leq t \leq T$$ 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 $\theta(t)$ as $\epsilon \rightarrow 0.$

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B. L. S. Prakasa Rao. 2026-02-18. Nonparametric estimation of linear multiplier for processes driven by a Hermite process. https://arxiv.org/abs/2602.16223

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