  This paper discusses properties of a Doubly Stochastic Poisson Process (DSPP)
where the intensity process belongs to a class of affine diffusions. For any
intensity process from this class we derive an analytical expression for
probability distribution functions of the corresponding DSPP. A specification
of our results is provided in a particular case where the intensity is given by
one-dimensional Feller process and its parameters are estimated by Kalman
filtering for high frequency transaction data.
