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Estimation and filtering on a doubly stochastic poisson process

Author

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  • Mariano J. Valderrama
  • Francisco Jimenez
  • Ramon Gutierrez
  • Alfredo Martinez‐Almecija

Abstract

An explicit formula for the characteristic function of a doubly stochastic Poisson process is derived in this paper by means of the harmonic decomposition of its intensity function that we suppose to be Gaussian. The statistical moments are then obtained, as well as the sample function density of the process. These results are applied to estimate the parameters of several well‐known processes. Finally, a linear filtering procedure for the intensity function is developed and the algorithm is implemented by computers.

Suggested Citation

  • Mariano J. Valderrama & Francisco Jimenez & Ramon Gutierrez & Alfredo Martinez‐Almecija, 1995. "Estimation and filtering on a doubly stochastic poisson process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 13-24, March.
  • Handle: RePEc:wly:apsmda:v:11:y:1995:i:1:p:13-24
    DOI: 10.1002/asm.3150110104
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