Edgeworth expansion for the integrated Levy driven Ornstein-Uhlenbeck process

TL;DR

This paper establishes the validity of Edgeworth expansions of any order for the integrated Levy driven Ornstein-Uhlenbeck process using Malliavin calculus, providing explicit formulas for the expansion coefficients due to the model's structure.

Contribution

It proves the Edgeworth expansion for the process and derives explicit formulas for the coefficients, advancing theoretical understanding of Levy-driven stochastic processes.

Findings

Edgeworth expansion verified for the process

Coefficients of the expansion are given in closed form

Expansion holds for any order

Abstract

We verify the Edgeworth expansion of any order for the integrated ergodic Levy driven Ornstein-Uhlenbeck process, applying a Malliavin calculus with truncation over the Wiener-Poisson space. Due to the special structure of the model, the coefficients of the expansion can be given in a closed form.