Optimal approximation of Skorohod integrals

TL;DR

This paper establishes the optimal approximation rate for Skorohod integrals of regular integrands, extending known results for Itô integrals and introducing new proof techniques due to the lack of adaptedness.

Contribution

It introduces a novel approach using S-transform and Wick-analytic functionals to analyze Skorohod integrals, generalizing approximation results beyond Itô integrals.

Findings

Determined the optimal approximation rate for Skorohod integrals.

Extended approximation results from Itô to Skorohod integrals.

Developed new proof techniques involving S-transform and Wiener chaos reformulation.

Abstract

In this manuscript, we determine the optimal approximation rate for Skorohod integrals of sufficiently regular integrands. This generalizes the optimal approximation results for It\^o integrals. However, without adaptedness and the It\^o isometry, new proof techniques are required. The main tools are a characterization via S-transform and a reformulation of the Wiener chaos decomposition in terms of Wick-analytic functionals.