Abstract
The subthreshold behavior of the somal-membrane potential of a single neuron is modeled as a semimartingale. This model extends all Itô-type stochastic neuronal models which have been treated in the literature. The theory of optimal estimating functions is applied to estimate the parameters of the proposed model. This is a likelihood-free method which does not require imposing any distributional assumptions on the noise or driving process. This method includes conditional least squares, quasi-least squares as special cases. Under regularity conditions together with distributional assumptions, it leads to the maximum likelihood method.
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