Polynomials under Ornstein-Uhlenbeck noise and an application to inference in stochastic Hodgkin-Huxley systems

03/30/2020

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by   Reinhard Höpfner, et al.

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We discuss estimation problems where a polynomial is observed under Ornstein Uhlenbeck noise over a long time interval. We prove local asymptotic normality (LAN) and specify asymptotically efficient estimators. We apply this to the following problem: feeding noise into the classical (deterministic) Hodgkin Huxley model of neuroscience, we are interested in asymptotically efficient estimation of the parameters of the noise process.