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A Monte Carlo method for filtering a marked doubly stochastic Poisson process

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Abstract

The author provides an approximated solution for the filtering of a state-space model, where the hidden state process is a continuous-time pure jump Markov process and the observations come from marked point processes. Each state k corresponds to a different marked point process, defined by its conditional intensity function λ k (t). When a state is visited by the hidden process, the corresponding marked point process is observed. The filtering equations are obtained by applying the innovation method and the integral representation theorem of a point process martingale. Since the filtering equations belong to the family of Kushner–Stratonovich equations, an iterative solution is calculated. The theoretical solution is approximated and a Monte Carlo integration technique employed to implement it. The sequential method has been tested on a simulated data set based on marked point processes widely used in the statistical analysis of seismic sequences: the Poisson model, the stress release model and the Etas model.

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Authors and Affiliations

  1. CNR, Institute of Applied Mathematics and Information Technology, Via E. Bassini 15, 20133, Milan, Italy

    Elisa Varini

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  1. Elisa Varini
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Correspondence to Elisa Varini.

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Varini, E. A Monte Carlo method for filtering a marked doubly stochastic Poisson process. Stat. Meth. & Appl. 17, 183–193 (2008). https://doi.org/10.1007/s10260-007-0051-y

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  • DOI: https://doi.org/10.1007/s10260-007-0051-y

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