On the estimation of the stochastic intensity and the parameters of neyman-scott trigger processes

Abstract

In this paper we are concerned with a class of simple point processes, whose unobservable stochastic intensity is a shot-noise process. We derive a stochastic equation for the conditional moment generating function of the intensity, which can be solved in a recursive way. This yields explicit expression for the minimum variance estimate of the intensity as well as the likelihood ration with respect to the reference measure, on the basis of point process observations.

Keywords:

• Primary 93 E 10
• secondary 62 M 09
• 62 M 99
• 60 G 35
• NEYMAN-SCOTT trigger processes
• doubly stochastic POISSON processes
• point processes
• non-linear filtering