Estimation of the Rate of a Doubly-Stochastic Time-Space Poisson Process.
Estimation of the Rate of a Doubly-Stochastic Time-Space Poisson Process.
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1985
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Abstract
We consider the problem of estimating the rate of a doubly- stochastic, time-space Poisson process when the observations are restricted to a region D subset of R^2. In the general case, we obtain a representation of the minimum mean-square-error (MMSE) estimate in terms of the conditional characteristic function of an underlying state process. In the case D=R^2, we extend a known result to compute the MMSE estimate explicitly. For a special form of the rate process, a well-defined integral equation is presented which defines the linear MMSE estimate of the rate.