ANALYTICITY OF POISSON-DRIVEN STOCHASTIC-SYSTEMS

Let psi be a functional of the sample path of a stochastic system driven by a Poisson process with rate lambda. It is shown in a very general setting that the expectation of psi, E(lambda)[psi], is an analytic function of lambda under certain moment conditions. Instead of following the straightforward approach of proving that derivatives of arbitrary order exist and that the Taylor series converges to the correct value, a novel approach consisting in a change of measure argument in conjunction with absolute monotonicity is used. Functionals of non-homogeneous Poisson processes and Wiener processes are also considered and applications to light traffic derivatives are briefly discussed.