Chapter 6 - Simple Point Processes

Abstract

This chapter presents problems of inference for Poisson processes and certain Levy processes via their imbedded compound Poisson processes. It discusses homogeneous Poisson process, nonhomogeneous Poisson process, and compound Poisson process and problems of inference for such Poisson process. A compound Poisson process can be described as follows: Jumps occur according to a Poisson process with intensity, λ(t), and by denoting Yi for the magnitude of the ith jump, it is assumed that {Yi} are independent, identically distributed random variables that are also independent of the Poisson process {Xt, t ≥ 0} that produces these jumps. The chapter describes problems of inference for compound Poisson processes via those for gamma and stable processes.