Reference for Poisson point process

Question

I'm looking for a good reference book for PPP (Poisson point process) and the stochastic integration theory with regard to PPP.

I have tried "Stochastic Differential Equations and Diffusion Process" written by Shinzo Watanabe & the lecture notes for Stochastic Analysis written by Prof Andreas Eberle.

But I think they are both not strictly enough to introduce PPP in a mathematical way. (Indeed some conclusions seemed impossible under the former assumptions given in this two books!)

So I wonder if there is any notes or books which can provide a "strict" introduction of PPP and its stochastic integration theory.

Answer 1

Poisson Processes by J.F.C. Kingman (Oxford University Press, 1993) is an excellent introduction.

A deeper dive can be found in Lectures on the Poisson Process by G. Last and M. Penrose (Cambridge University Press, 2018).