Stein factors for variance-gamma approximation in the Wasserstein and Kolmogorov distances

TL;DR

This paper derives new bounds for the variance-gamma Stein equation solutions, enabling accurate approximation in Wasserstein and Kolmogorov distances, with applications to Wiener-Itô integrals.

Contribution

It provides the first comprehensive bounds valid for all variance-gamma parameters, facilitating improved approximation accuracy in probability metrics.

Findings

New bounds for VG Stein equation solutions in Wasserstein and Kolmogorov metrics

Explicit error bounds in a six moment theorem for VG approximation

Applicable to all parameter values of the variance-gamma distribution

Abstract

We obtain new bounds for the solution of the variance-gamma (VG) Stein equation that are of the correct form for approximations in terms of the Wasserstein and Kolmorogorov metrics. These bounds hold for all parameters values of the four parameter VG class. As an application we obtain explicit Wasserstein and Kolmogorov distance error bounds in a six moment theorem for VG approximation of double Wiener-It\^{o} integrals.