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Semiparametric Estimation of the State of a Dynamical System with Small Noise

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Abstract

We consider the problem of estimation of the state of a perturbed dynamical system by observing the trajectory of a diffusion process with known small diffusion coefficient. The drift coefficient is supposed to be an unknown regular function. Asymptotic minimax lower bounds for the risk of any estimator of the state are derived and the notion of efficiency is introduced. The naïve estimator for this problem is proposed and its basic properties are discussed. It emerges that this estimator is asymptotically efficient.

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Authors and Affiliations

  1. Dipartimento di Economia Politica ed Aziendale, Università di Milano, Via del Conservatorio 7, I-20122, Milano, Italy

    Stefano Maria Iacus

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  1. Stefano Maria Iacus
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Iacus, S.M. Semiparametric Estimation of the State of a Dynamical System with Small Noise. Statistical Inference for Stochastic Processes 3, 277–288 (2000). https://doi.org/10.1023/A:1009929415011

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