The semiclassical formalism for integrated statistics in photoelectron counting is compared with a method of population monitoring for a single-mode cavity field evolving according to an arbitrary Markov process. Equations governing the exact integrated statistics in the two approaches are shown to be identical up to a single-photon loss process associated with the photodetection. Specific examples are provided, illustrating the relation of these methods to explicitly second-quantized formulations.
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T.J. Shepherd (1984) studied this question.