What is a good reference for compound Poisson processes?

Question

I've seen a couple of descriptions of the basic statistics of a compound Poisson process, basically just simple statements about how to compute the mean and variance given the mean and variance of the underlying processes. Unfortunately I haven't found anything which I feel comfortable citing in a professional context.

Can anybody recommend a good desk reference that would cover compound Poisson processes/distributions?

Preferably it would be general enough to serve as a good desk reference on statistics for an engineer (with a tendency to do a lot of numerical analysis), rather than focusing purely on compound processes. Bonus points if it also gives a good outline of Bayesian inference in general.

Answer 1

This book on Non-Life Insurance Mathematics might actually work for you. It is oriented towards applications, though not engineering applications, but it is completely theoretically sound. If I am not mistaken, there is something in the book on Bayes estimation too.

Note that you should look for the Cramèr-Lundberg model in the context of the book to find the compound Poisson process.