Properties of Doubly Stochastic Poisson Process with affine intensity

Details Properties of Doubly Stochastic Poisson Process with affine intensity Properties of Doubly Stochastic Poisson Process with affine intensity

2011-09-13

arxiv.org/abs/1109.2884v2

Mathematics

Statistics Theory

Scientific paper

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.

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