The capacity of a Poisson-type channel subject both to peak amplitude and average energy constraints is calculated, and its relation to the cutoff rate given by Snyder and Rhodes is determined in the "very noisy" case.

The innovations approach in communication theory solves the signal detection problem in terms of a related nonlinear filter. Simulation data is presented which shows that, at least for one example, using the appropriate linear filter instead results in a very small loss of detection power even though the variance of the linear filter is considerably greater than that of the nonlinear one. The results also illuminate the role of "predictable processes" in communication theory.

An explicit solution is given of the nonlinear filtering problem of estimating the time of "disorder" of a counting process of very general type.

We apply some recent results in martingale theory and the innovations method to obtain the evolution of the conditional mean and conditional density of a process that modulates the rate of a counting process.