A new firing paradigm for integrate and fire stochastic neuronal models

A new definition of firing time is given in the framework of In- tegrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the mem- brane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved.