On the error estimate for cubature on Wiener space

TL;DR

This paper refines the error estimate for the cubature on Wiener space algorithm, removing the need for an extra drift assumption by adapting Kusuoka's analysis, and improves existing bounds.

Contribution

It provides a more general error estimate for the cubature on Wiener space method without extra drift assumptions, enhancing previous theoretical results.

Findings

Error bounds are extended without additional drift assumptions.

The bounds derived in Kusuoka's analysis are slightly sharpened.

The approach simplifies the theoretical understanding of the algorithm's accuracy.

Abstract

It was pointed out in Crisan, Ghazali [2] that the error estimate for the cubature on Wiener space algorithm developed in Lyons, Victoir [11] requires an additional assumption on the drift. In this note we demonstrate that it is straightforward to adopt the analysis of Kusuoka [7] to obtain a general estimate without an additional assumptions on the drift. In the process we slightly sharpen the bounds derived in [7].