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In this paper, we provide a complete mathematical construction for astochastic leaky-integrate-and-fire model (LIF) mimicking the interspikeinterval (ISI) statistics of a stochastic FitzHugh-Nagumo neuron model (FHN) inthe excitable regime, where the unique fixed point is stable. Under specifictypes of noises, we prove that there exists a global random attractor for thestochastic FHN system. The linearization method is then applied to estimate thefiring time and to derive the associated radial equation representing a LIFequation. This result confirms the previous prediction in [Ditlevsen, S. andGreenwood, P. (2013). The Morris-Lecar neuron model embeds a leakyintegrate-and-fire model. Journal of Mathematical Biology, 67(2):239-259] forthe Morris-Lecar neuron model in the bistability regime consisting of a stablefixed point and a stable limit cycle.

Stochastic FitzHugh-Nagumo neuron model in excitable regime embeds a leaky integrate-and-fire model