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A Point Process Approach to Filtered Processes

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  • Julien Michel

    (Unité de Mathématiques Pures et Appliquées—UMR 5669, ENS Lyon)

Abstract

We consider some models of filtered point processes such as those developped in Yue and Hashino (2001), and rephrase them in terms of point processes. We derive from this formulation some estimates for the probability of overflow in a rainfall process. This method allows us by considering a non deterministic model of filtering to compute some characteristics of the compound models of Cowpertwait (1994), Phelan (1991), and Rodriguez-Iturbe et al. (1987, 1988). A spatial version of this point process is also studied, using an analogy with the boolean model of stochastic geometry we compute bounds for the probability of dryness in a compound rainfall process.

Suggested Citation

  • Julien Michel, 2004. "A Point Process Approach to Filtered Processes," Methodology and Computing in Applied Probability, Springer, vol. 6(4), pages 423-440, December.
    • Handle: RePEc:spr:metcap:v:6:y:2004:i:4:d:10.1023_b:mcap.0000045089.40163.c7
    DOI: 10.1023/B:MCAP.0000045089.40163.c7
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