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arXiv · 1803.01032

Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion

Yaozhong Hu·David Nualart·Hongjuan Zhou
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Abstract

We derive the strong consistency of the least squares estimator for the drift coefficient of a fractional stochastic differential system. The drift coeffcient is one-sided dissipative Lipschitz and the driving noise is additive and fractional with Hurst parameter $H \in (\frac{1}{4}, 1)$. We assume that continuous observation is possible. The main tools are ergodic theorem and Malliavin calculus. As a by-product, we derive a maximum inequality for Skorohod integrals, which plays an important role to obtain the strong consistency of the least squares estimator.

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Yaozhong Hu, David Nualart, Hongjuan Zhou. 2018-03-02. Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion. https://arxiv.org/abs/1803.01032

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