  Event-scheduling algorithms can compute in continuous time the next
occurrence of points (as events) of a counting process based on their current
conditional intensity. In particular event-scheduling algorithms can be adapted
to perform the simulation of finite neuronal networks activity. These
algorithms are based on Ogata's thinning strategy \cite{Oga81}, which always
needs to simulate the whole network to access the behaviour of one particular
neuron of the network. On the other hand, for discrete time models, theoretical
algorithms based on Kalikow decomposition can pick at random influencing
neurons and perform a perfect simulation (meaning without approximations) of
the behaviour of one given neuron embedded in an infinite network, at every
time step. These algorithms are currently not computationally tractable in
continuous time. To solve this problem, an event-scheduling algorithm with
Kalikow decomposition is proposed here for the sequential simulation of point
processes neuronal models satisfying this decomposition. This new algorithm is
applied to infinite neuronal networks whose finite time simulation is a
prerequisite to realistic brain modeling.
