Stability of Age Dependent Hawkes Processes

In recent years hawkes processes have been considered as a model for functional connectivity of neurons in the brain. The age dependent hawkes process is a modification of the hawkes process which is able to incorporate the refractory period into the model. In this talk we discuss existence and uniqueness of a stationary version of the ADHP. Furthermore, we present conditions under which an ADHP couples with the stationary version. Finally we present a construction of regeneration times for the ADHP.

Talk in english.