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 . Events of type A will precipitate events of type B only when they move the state process to some critical region, say. In parallel, as each event occurs, the state process transitions to a new value according to transition probabilities that vary with the event type. We prove that such dynamics are equivalent to an intensity processof a specific product form .
After revision:  A particular example of a hybrid marked point process is a state-dependent Hawkes process, a state-dependent Hawkes process that interacts with its state process .