Factorial moment expansion for stochastic systems

AbstractFor a given functional of a simple point process, we find an analogue of Taylor's theorem for its mean value. The terms of the expansion are integrals of some real functions with respect to factorial moment measures of the point process. The remainder term is an integral of some functional with respect to a higher order Campbell measure. A special case of this expansion is Palm-Khinchin formula. The results complement previous studies of Reiman and Simon (1989), Baccelli and Brémaud (1993) and shed new light on light traffic approximations of Daley and Rolski (1994), Błaszczyszyn and Rolski (1993)