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 nonexplosive 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.

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

CENTANNI, Silvia;MINOZZO, Marco;
2011-01-01

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, specified as a positive function of another nonexplosive 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.
2011
Cox process; Marked point process; Particle filtering; Sequential Monte Carlo method; Shot noise process
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/385449
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact