Before revision: We introduce the class of hybrid marked point processes , which incorporate a state process that interacts with past-dependent events.
After revision: We introduce the class of hybrid marked point processes that encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class provides a unified treatment of such existing processes, it also contains new processes with complex dynamics. These marked point processes are defined implicitly via their intensity and are endowed with a state process that interacts with past-dependent events.