Polynomials under Ornstein–Uhlenbeck noise and an application to inference in stochastic Hodgkin–Huxley systems
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Abstract
We discuss estimation problems where a polynomial s→∑ℓi=0ϑisi with strictly positive leading coefficient 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 dYt into the classical (deterministic) Hodgkin–Huxley model in neuroscience, with Yt=ϑt+Xt and X some Ornstein–Uhlenbeck process with backdriving force τ, we have asymptotically efficient estimators for the pair (ϑ,τ); based on observation of the membrane potential up to time n, the estimate for ϑ converges at rate n3−−−√.
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Statistical inference for stochastic processes, 24, Springer Science + Business Media B.V., Dordrecht, 2021, https://doi.org/10.1007/s11203-020-09226-0