To date, Mixed Poisson processes have been studied by scientists primarily interested in either insurance mathematics or point processes. Work in one area has often been carried out without knowledge of the other area. Mixed Poisson Processes is the first book to combine and concentrate on these two themes, and to distinguish between the notions of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.
Introduction
The Mixed Poisson Distributions
Some Basic Concepts
The Mixed Poisson Process
Some Related Processes
Cox Processes
Gauss-Poisson Processes
Mixed Renewal Processes
Characterization of Mixed Poisson Processes
Reliability Properties of Mixed Poisson Processes
Characterization within Birth Processes
Characterization within Stationary Point Processes
Characterization within General Point Processes
Compound Mixed Poisson Distributions
Compound Distributions
Exponential Bounds
Asymptotic Behaviour
Recursive Evaluation
The Risk Business
The Claim Process
Ruin Probabilities
Biography
Jan Crandall is Professor of Mathematical Statistics in the Department of Mathematics at the Royal Institute of Technology, Stockholm, Sweden.
