A multi-dimensional central limit bound and its application to the Euler approximation of Lévy-SDEs

Xiling Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

In the one-dimensional case Rio (Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009) 802–817) gave a concise bound for the central limit theorem in the Vaserstein distances, which is a ratio between some higher moments and some powers of the variance. As a corollary, it gives an estimate for the normal approximation of the small jumps of Lévy processes, and Fournier (ESAIM: PS 15 (2011) 233–248) applied that to the Euler approximation of stochastic differential equations driven by the Lévy noise. It will be shown in this article that following Davie’s idea in (Polynomial Perturbations of Normal Distributions. Available at: www.maths.ed.ac.uk/~sandy/polg.pdf (2016)), one can generalise Rio’s result to the multidimensional case, and have higher-order approximation via the perturbed normal distributions, if Cramér’s condition and a slightly stronger moment condition are assumed. Fournier’s result can then be partially recovered.
Original languageEnglish
Pages (from-to)112-135
Number of pages24
JournalESAIM: Probability and Statistics
Volume23
Early online date26 Mar 2019
Publication statusE-pub ahead of print - 26 Mar 2019

Fingerprint

Dive into the research topics of 'A multi-dimensional central limit bound and its application to the Euler approximation of Lévy-SDEs'. Together they form a unique fingerprint.

Cite this