A theoretical connection between the Noisy Leaky integrate-and-fire and the escape rate models: The non-autonomous case

¹ École Normale Supérieure, Group for Neural Theory, 45 Rue d’Ulm, 75005 Paris, France.
² INRIA team Carmen, INRIA Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, 33405 Talence cedex, France.
³ Department of Mathematics and Informatics, “Gheorghe Asachi” University of Iaşi, Bulevardul Carol I 11, 700506 Iaşi, Romania.
⁴ Interdisciplinary Research Department, Field - Sciences, “Alexandru Ioan Cuza” University of Iaşi, Lascăr Catargi 54, Iaşi, Romania.

^* Corresponding author: tarniceriuoana@yahoo.co.uk

Received: 8 July 2019
Accepted: 27 April 2020

Abstract

Finding a mathematical model that incorporates various stochastic aspects of neural dynamics has proven to be a continuous challenge. Among the different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most popular. These two models are generally thought to express different noise action over the neural cell. In this paper we investigate the link between the two formalisms in the case of a neuron subject to a time dependent input. To this aim, we introduce a new general stochastic framework. As we shall prove, our general framework entails the two already existing ones. Our results have theoretical implications since they offer a general view upon the two stochastic processes mostly used in neuroscience, upon the way they can be linked, and explain their observed statistical similarity.