As well as having complete knowledge of the future, a superprophet can also alter the order of observation as it is presented to a player without foresight, whose strategy is known to the prophet. It is shown that a superprophet can only do twice as well as his counterpart, if the underlying random sequence is independent.

This paper provides a direct approach to obtaining formulas for derivatives of functionals of point processes in rare perturbation analysis ([2], [6]). Results are obtained for arbitrary (not necessarily stationary) point processes in and d, d 2, under transparent conditions, close to minimal. Formulas for higher-order derivatives allow one to construct asymptotical expansions. The results can be useful in sensitivity analysis, in light traffic theory for queues and for computation by simulation of derivatives at positive intensity, while the computation of the derivatives via statistical estimation of the functional itself and its increments usually gives poor results.

The so-called ‘Swiss Army formula', derived by Brémaud, seems to be a general purpose relation which includes all known relations of Palm calculus for stationary stochastic systems driven by point processes. The purpose of this article is to present a short, and rather intuitive, proof of the formula. The proof is based on the Ryll–Nardzewski definition of the Palm probability as a Radon-Nikodym derivative, which, in a stationary context, is equivalent to the Mecke definition.