Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-5803
Authors: Höpfner, Reinhard
Title: Polynomials under Ornstein–Uhlenbeck noise and an application to inference in stochastic Hodgkin–Huxley systems
Online publication date: 11-May-2021
Year of first publication: 2021
Language: english
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−−−√.
DDC: 510 Mathematik
510 Mathematics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
ROR: https://ror.org/023b0x485
DOI: http://doi.org/10.25358/openscience-5803
Version: Published version
Publication type: Zeitschriftenaufsatz
License: CC BY
Information on rights of use: https://creativecommons.org/licenses/by/4.0/
Journal: Statistical inference for stochastic processes
24
Pages or article number: 35
59
Publisher: Springer Science + Business Media B.V.
Publisher place: Dordrecht
Issue date: 2021
ISSN: 1572-9311
Publisher URL: https://doi.org/10.1007/s11203-020-09226-0
Publisher DOI: 10.1007/s11203-020-09226-0
Appears in collections:JGU-Publikationen

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