Gaussian approximation for the small jumps of Lévy processes

26.11.2018, 10:15  –  Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Dr. Ester Mariucci

It is common practice to treat small jumps of a Lévy process as Wiener noise and thus to approximate their marginals by means of their corresponding Gaussian distributions.

However, results that allow to quantify the goodness of such an approximation according to a given metric are rare. In this talk we will focus on two metrics: the Wasserstein distance of order p and the total variation distance. 

Upper bounds for these metrics are discussed. In particular, sharp and non asymptotic bounds for a Gaussian approximation for jumps of infinite activity are presented. The theory is illustrated by concrete examples and an application to statistical lower bounds. This is based on joint works with Markus Reiss and with Alexandra Carpentier and Céline Duval.