Intermittency in the small-time behavior of Lévy processes

Danijel Grahovac

Published 2019-12-09Version 1

Limit theorems for L\'evy processes in the small-time limit have been established recently in Ivanovs (2018). In this paper we consider convergence of moments in these limit theorems. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds typically only up to some critical moment order and higher order moments decay at different rate. Such behavior is known as intermittency and has been encountered in some limit theorems. As a consequence, we show that a L\'evy process may exhibit different rates of decay in the small-time limit.