Estimation of the Rate of a Doubly-Stochastic Time-Space Poisson Process.

摘要

The authors consider the problem of estimating the rate of a doubly- stochastic, time-space Poisson process when the observations are restricted to a region D reflex subset contained in R(exp 2). In the general case, they 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(exp 2), they 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.