  This paper presents a simulation-based framework for sequential inference
from partially and discretely observed point process (PP's) models with static
parameters. Taking on a Bayesian perspective for the static parameters, we
build upon sequential Monte Carlo (SMC) methods, investigating the problems of
performing sequential filtering and smoothing in complex examples, where
current methods often fail. We consider various approaches for approximating
posterior distributions using SMC. Our approaches, with some theoretical
discussion are illustrated on a doubly stochastic point process applied in the
context of finance.
