Continuous time filtering for a class of marked doubly stochastic Poisson processes

Marco Minozzo () and Silvia Centanni ()
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Silvia Centanni: Department of Economics (University of Verona)

No 23/2011, Working Papers from University of Verona, Department of Economics

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, specified as a 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.

Keywords: Cox process; Marked point process; Particle filtering; Sequential Monte Carlo method; Shot noise process (search for similar items in EconPapers)
JEL-codes: C51 (search for similar items in EconPapers)
Pages: 21
Date: 2011-12
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Published in Manoscritto sottomesso per pubblicazione su "Computational Statistics and Data Analysis".

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