ASYMPTOTIC EXPANSIONS FOR FUNCTIONALS OF DILATION OF POINT-PROCESSES

This paper provides a direct approach to obtaining formulas for deriva tives of functionals of point processes in rare perturbation analysis ([2], [6]). Results are obtained for arbitrary (not necessarily statio nary) point processes in R and R(d), d greater than or equal to 2, und er transparent conditions, close to minimal. Formulas for higher-order derivatives allow one to construct asymptotical expansions. The resul ts can be useful in sensitivity analysis, in light traffic theory for queues and for computation by simulation of derivatives at positive in tensity, while the computation of the derivatives via statistical esti mation of the functional itself and its increments usually gives poor results.