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Updated: Aug 14, 2026

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
Published on: March 2, 2015
A stochastic model and a functional central limit theorem for information processing in large systems of neurons
Reinhard Höpfner1, Klaus Brodda
1Institute of Mathematics, University of Mainz, Staudingerweg 9, 55099, Mainz, Germany. hoepfner@mathematik.uni-mainz.de
Abstract:
The paper deals with information transmission in large systems of neurons. We model the membrane potential in a single neuron belonging to a cell tissue by a non time-homogeneous Cox-Ingersoll-Ross type diffusion; in terms of its time-varying expectation, this stochastic process can convey deterministic signals. We model the spike train emitted by this neuron as a Poisson point process compensated by the occupation time of the membrane potential process beyond the excitation threshold. In a large system of neurons 1 < or = i < or = N processing independently the same deterministic signal, we prove a functional central limit theorem for the pooled spike train collected from the N neurons. This pooled spike train allows to recover the deterministic signal, up to some shape transformation which is explicit.
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