The asymptotic expansion of the regular discretization error of It\^o integrals

TL;DR

This paper develops an Edgeworth-type expansion for the discretization error in Itô integrals, using a novel approach based on the anticipating Itô formula to explicitly compute the expansion terms.

Contribution

It introduces a new method utilizing the anticipating Itô formula to explicitly derive the asymptotic expansion of the discretization error in Itô integrals.

Findings

Explicit asymptotic expansion formula derived

New approach simplifies computation of expansion terms

Enhances understanding of discretization errors in stochastic calculus

Abstract

We study a Edgeworth-type refinement of the central limit theorem for the discretizacion error of It\^o integrals. Towards this end, we introduce a new approach, based on the anticipating It\^o formula. This alternative technique allows us to compute explicitly the terms of the corresponding expansion formula.