I am looking for a modern, graduate level, rigorous book on temporal point processes which also treats self-correcting point processes, and self-exciting point processes.


It would be even more interesting if the book was also pointing me to some research questions in the field.



Graduate-level reference on temporal point processes
You can briefly read a short introduction to decide whether you are interested in the theoretic side or application side of the research subject. Say [Rasmussen's Notes](http://people.math.aau.dk/~jgr/teaching/punktproc11/tpp.pdf). 


If you are more interested in the theory, there is a two-volume standard text on theory of point processes. It includes a panoramic discussion on temporal/spatial process in Chap 14,15.



> 
> Daley, Daryl J., and David Vere-Jones. An introduction to the theory
>  of point processes: volume I&II, 2ed, Springer, 2007.
> 
> 
> 


If you are more interested in the application, there is a very popular book [ABG](https://link.springer.com/book/10.1007%2F978-0-387-68560-1) discusses a variety of applications of point processes in survival analysis.



> 
> Aalen, Odd, Ornulf Borgan, and Hakon Gjessing. Survival and event
>  history analysis: a process point of view. Springer Science & Business
>  Media, 2008.
> 
> 
> 


