Abstract

Compound Poisson processes are the building blocks of models for occurrence of random events at random times. They are used in a myriad of applications ranging from queueing theory and seismology to insurance and finance, so efficient estimation of their characteristics is of great importance. We will speak of our recent developments in this area, including a Donsker theorem for the distribution of the size of the events. The talk is aimed at students with undergraduate level of probability but no necessarily any exposure to the topics below, as this talk will serve as a quick introduction to them. We are planning to:

i) introduce the CPP and its applications; ii) describe the non-parametric estimation problem and its relationship to non-linear inverse problems; iii) construct an estimator of the aforementioned distribution and state some basic results to build intuition; iv) introduce the classical Glivenko-Cantelli and Donsker theorems from empirical process theory; v) state our Donsker theorem and its applications and mention extensions and related literature;