Probabilistic Spiking Neuronal Nets: Neuromathematics for the Computer Era

This book provides a self-contained introduction to a new class of shastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a shastic process with a memory of variable length. Several mathematical tools are put to use, such as Markov chains, shastic chains having memory of variable length, point processes having shastic intensity, Hawkes processes, random graphs, mean field limits, perfect sampling algorithms, the Conte...