PalestranteProf. Dr. Naoki Masuda - Universidade de Bristol

Resumo: The Gillespie algorithm is a tool to exactly simulate event-driven stochastic dynamics (interacting point processes). Its applications include systems of biochemical reactions or earthquakes, networks of queuing processes or spiking neurons, and epidemic and opinion formation processes on networks. As recent research on temporal networks has demonstrated, inter-event times of various human activities, among others, obey long-tailed distributions, violating the Poissonian assumption underlying the basic Gillespie algorithm. Starting from general introduction to temporal networks, I will present a new Gillespie algorithm for renewal processes which are not necessarily Poisson processes. The algorithm crucially exploits properties of the Laplace transform. It is applicable to renewal processes whose survival function of inter-event times is a completely monotone function. It works faster than a previously proposed algorithm and is exact for an arbitrary number of processes running in parallel.