Explict Formulas for the Divergence Operator in Isonormal Gaussian Space

Abstract: In this paper, we first derive some explicit formulas for the computation of the n-th order divergence operator in Malliavin calculus in the one-dimensional case. We then extend these results to the case of isonormal Gaussian space. Our results generalize some of the known results for the divergence operator. Our approach in deriving the formulas is new and simple.