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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.

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    $\begingroup$ Why was this closed? It looks like a perfectly normal reference request to me. $\endgroup$ – Nate Eldredge Apr 25 '17 at 18:18
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    $\begingroup$ I have the same confusion as @NateEldredge . This post looks fine to me and temporal point process is not exactly sharing the same reference as general point processes. They have some special methods when doing survival analysis. I edited the OP's title and tag. $\endgroup$ – Henry.L Apr 25 '17 at 18:41
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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.

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 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.

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