We model a sequence of events by using a class of marked doubly stochastic Poisson processes where the intensity is given by a generalization of the classical shot noise process, that is a given positive function of another non-explosive marked point process. To filter the unobservable intensity, a time recursion is constructed to characterize a sequence of filtering distributions, that is, the conditional distributions of the intensity, given the past observations, evaluated at opportunely chosen time instants. To approximate this sequence, we consider a discrete approximation with random support by implementing a particle filter, in which we draw recursively from each filtering distribution. In the case in which the pair formed by the marked point process and by the intensity is a Markov process, this filtering recursion can be related to the classical filtering theory.

Particle filtering in a class of marked doubly stochastic Poisson processes

CENTANNI, Silvia;MINOZZO, Marco;
2005-01-01

Abstract

We model a sequence of events by using a class of marked doubly stochastic Poisson processes where the intensity is given by a generalization of the classical shot noise process, that is a given positive function of another non-explosive marked point process. To filter the unobservable intensity, a time recursion is constructed to characterize a sequence of filtering distributions, that is, the conditional distributions of the intensity, given the past observations, evaluated at opportunely chosen time instants. To approximate this sequence, we consider a discrete approximation with random support by implementing a particle filter, in which we draw recursively from each filtering distribution. In the case in which the pair formed by the marked point process and by the intensity is a Markov process, this filtering recursion can be related to the classical filtering theory.
2005
Cox process; Kushner-Stratonovich equation; Marked point process; Sequential Monte Carlo method; Shot noise process
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/313894
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