Before revision:  A particular example of a hybrid marked point process is a state-dependent Hawkes process, where events can exhibit self- or cross-excitation effects, like in classical Hawkes processes, but these effects can now also depend on the state process .
After revision:  In fact, this property completely characterises the class of hybrid marked point process is a state-dependent Hawkes process, where events can exhibit self- or cross-excitation effects, like in classical Hawkes processes, but these effects can now also depend on the state process .