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The normal approximation rate for the drift estimator of multidimensional diffusions

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Abstract

We consider the problem of the density and drift estimation by the observation of a trajectory of an \({\mathbb{R}^{d}}\)-dimensional homogeneous diffusion process with a unique invariant density. We construct estimators of the kernel type based on discretely sampled observations and study their asymptotic distribution. An estimate of the rate of normal approximation is given.

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Authors and Affiliations

  1. Department of Mathematics, Statistics, Computer Science and Appplications, Bergamo University, via dei Caniana 2, 24127, Bergamo, Italy

    Annamaria Bianchi

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  1. Annamaria Bianchi
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Correspondence to Annamaria Bianchi.

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Bianchi, A. The normal approximation rate for the drift estimator of multidimensional diffusions. Stat Inference Stoch Process 12, 251–268 (2009). https://doi.org/10.1007/s11203-008-9032-5

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  • DOI: https://doi.org/10.1007/s11203-008-9032-5

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