Anders Tolver Jensen,
Københavns universitet
	
Inference for doubly stochastic Poisson processes

Abstract:

The doubly stochastic Poisson process (DSPP) is a flexible class of
point processes with a conditionally Poisson structure given an
unobservable intensity. In this talk we discuss how the moments of the
invariant distribution of the latent intensity may be consistently
estimated from a single observation of the counting process. The
result is given in a double asymptotic framework where the total
observation interval as well as the sampling frequency tends to
infinity at carefully chosen rates. We finally present two examples
that satisfy the conditions for the main result: the semi-Markov
modulated Poisson process and the DSPP driven by a shot noise process.