Formulas for the divergence operator in isonormal Gaussian space

S. Levental and P. Vellaisamy

Statistics & Probability Letters, 2023, vol. 194, issue C

Abstract: In this paper, we first derive some explicit formulas for the computation of the n-th order divergence operator in Malliavin calculus for 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.

Keywords: Binomial theorem; Divergence operator; Hermite polynomial; Malliavin derivative; Isonormal Gaussian space (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2022.109743

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