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System Modelling and Optimization pp 430–436Cite as

Nonlinear estimation problems of poisson cluster processes

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 84))

Abstract

Doubly stochastic Poisson processes whose unobservable intensity is a shot-noise process with random amplitude arise when each event of a primary Poisson process generates a random number of subsidiary events. We derive a stochastic partial differential equation for the unnormalized conditional moment generating function. This equation can be used for recursive compution of the minimum variance estimator of the unobservable intensity as well as the likelihood ratio with respect to the reference measure, on the basis of point process observations.

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Authors and Affiliations

  1. Institut für Mathematik u. Angewandte Statistik, Universität für Bodenkultur - Wien, Gregor Mendel-Straße 33, A - 1180, Wien, Austria

    Franz Konecny

Authors
  1. Franz Konecny
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A. Prékopa J. Szelezsáan B. Strazicky

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© 1986 Springer-Verlag

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Konecny, F. (1986). Nonlinear estimation problems of poisson cluster processes. In: Prékopa, A., Szelezsáan, J., Strazicky, B. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043866

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  • DOI: https://doi.org/10.1007/BFb0043866

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16854-6

  • Online ISBN: 978-3-540-47138-7

  • eBook Packages: Springer Book Archive

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