A calculus on Fock space and its probabilistic interpretations

We introduce on the Fock space Gamma(L-2(R+)) two operators del(-) and del(+) expressing the infinitesimal perturbations of random variables by rime changes in the Wiener and Poisson probabilistic interpretations of Gamma(L2(R+)). These operators have close connections with stochastic integration, regularity of laws, chaotic expansions and complement the annihilation and creation operators del(-) and del(+) that are related to perturbations by shifts of trajectories. (C) Elsevier, Paris.