Explict Formulas for the Divergence Operator in Isonormal Gaussian Space

TL;DR

This paper derives explicit formulas for the divergence operator in Malliavin calculus, extending known results to isonormal Gaussian spaces with a new, simple approach.

Contribution

It introduces a novel, straightforward method to compute the divergence operator in isonormal Gaussian spaces, generalizing previous formulas.

Findings

Explicit formulas for the n-th order divergence operator in one-dimensional case

Extension of formulas to isonormal Gaussian space

Simplified derivation approach

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.