Activity of any neuron with delayed feedback stimulated with Poisson stream is non-Markov

TL;DR

This paper proves that the output interspike interval stream of certain excitatory neurons with delayed feedback driven by Poisson input cannot be modeled as a Markov process of any order, highlighting complex temporal dependencies.

Contribution

It provides a rigorous proof that neuron output streams with delayed feedback under Poisson stimulation are inherently non-Markovian, advancing understanding of neural stochastic processes.

Findings

Output interspike intervals are non-Markovian for the studied neuron class.

Delayed feedback induces complex temporal dependencies.

The result applies to a broad class of excitatory neuron models.

Abstract

For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order. Keywords: spiking neuron; Poisson stochastic process; probability density function; delayed feedback; non-Markov stochastic process