Total variation distance for discretely observed Lévy processes: a Gaussian approximation of the small jumps

Orateur: Céline DUVAL
Localisation: Université Paris 5, France
Type: Matinées proba-stats
Site: UPEM
Salle: Salle 4B 107
Date de début: 05/07/2019 - 10:30
Date de fin: 05/07/2019 - 11:30

It is common to treat small jumps of Lévy processes as Wiener noise and to approximate its marginals by a Gaussian distribution. However, results that allow to quantify the goodness of this approximation according to a given metric are rare. We study what happens when the chosen metric is the total variation distance. Such a choice is motivated by its statistical interpretation; if the total variation distance between two statistical models converges to zero, then no test can be constructed to distinguish the two models and they are therefore asymptotically equally informative. We provide a Gaussian approximation for the small jumps of Lévy processes in total variation distance. Non-asymptotic bounds for the total variation distance between n discrete observations of small jumps of a Lévy process and the corresponding Gaussian distribution are given.