A continuous time stochastic model for biological neural nets

TL;DR

This paper introduces a novel continuous-time stochastic model for biological neural networks, extending previous discrete models, with methods for simulation and conditions for finite activity duration.

Contribution

It presents a new continuous-time stochastic framework for neural nets, building on prior models, with simulation techniques and criteria for finite lifespan.

Findings

Model can be simulated efficiently for simple decay functions

Provides conditions for almost sure finite time of activity cessation

Extends discrete models to continuous-time setting

Abstract

We propose a new stochastic model for biological neural nets which is a continuous time version of the model proposed by Galves and L\"ocherbach in [A. Galves and E. L\"ocherbach, "Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets", J. Stat. Phys. 151 (2013), no. 5, 896-921]. We also show how to computationally simulate such model for easy neuron potential decays and probability functions and characterize when the model has a finite time of death almost surely.