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arXiv · 1506.04731

Maximum likelihood drift estimation for the mixing of two fractional Brownian motions

Yuliya Mishura
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Abstract

We construct the maximum likelihood estimator (MLE) of the unknown drift parameter $\theta\in \mathbb{R}$ in the linear model $X_t=\theta t+\sigma B^{H_1}(t)+B^{H_2}(t),\;t\in[0,T],$ where $B^{H_1}$ and $B^{H_2}$ are two independent fractional Brownian motions with Hurst indices $\frac12<H_1<H_2<1.$ The formula for MLE is based on the solution of the integral equation with weak polar kernel.

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Yuliya Mishura. 2015-06-15. Maximum likelihood drift estimation for the mixing of two fractional Brownian motions. https://arxiv.org/abs/1506.04731

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