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State estimation for cox processes on general spaces

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  • Karr, Alan F.

Abstract

Let N be an observable Cox process on a locally compact space E directed by an unobservable random measure M. Techniques are presented for estimation of M, using the observations of N to calculate conditional expectations of the form E [M]A], where A is the [sigma]-algebra generated by the restriction of N to A. We introduce a random measure whose distribution depends on NA, from which we obtain both exact estimates and a recursive method for updating them as further observations become available. Application is made to the specific cases of estimation of an unknown, random scalar multiplier of a known measure, of a symmetrically distributed directing measure M and of a Markov-directed Cox process on . By means of a Poisson cluster representation, the results are extended to treat the situation where N is conditionally additive and infinitely divisible given M.

Suggested Citation

  • Karr, Alan F., 1983. "State estimation for cox processes on general spaces," Stochastic Processes and their Applications, Elsevier, vol. 14(3), pages 209-232, March.
    • Handle: RePEc:eee:spapps:v:14:y:1983:i:3:p:209-232
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    Cited by:

    1. R. Lechnerová & K. Helisová & V. Beneš, 2008. "Cox Point Processes Driven by Ornstein–Uhlenbeck Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 315-335, September.

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