I'm looking for references on the stochastic calculus of Poisson processes. My books tend to focus on derivative pricing, where Brownian motion reigns supreme. Maybe some jump-diffusion models thrown in in chapter 10, but that's not what I'm looking for.
I'd like to read a book that covers the Ito calculus of Poisson processes with random intensity and jump sizes, in a detailed way like all the derivatives books present Ito calculus. (Stochastic control would be a plus, but isn't necessary)