SCS

Abstract

This talk will consist of three parts. In the first part, I shall give a universal formula that summarizes the effect on the Bartlett spectrum of a stationary point process of various transformations of the latter (thinning, translation, filtering, clustering, jitter) and give the Bartlett spectrum of a Hawkes process with random fertility rate (joint work with Laurent Massouli\'e and Andrea Ridolfi). In the second part, I shall give an example of long range dependence that is ``intrinsic'' (not due to long dependence of the intensity process of a Cox process): the branching process without ancestor (joint work with Laurent Massouli\'e). Finally, I shall list a few open problems in the theory of Bartlett spectra.