Скачать или смотреть Multivariate CLT for Levy processes: convergence rates without moment assumptions

In this video I describe our new results on the equivalence of the finiteness of the second moment of a d-dimensional Levy process and the integrability at infinity of the convex distance (with respect to the scale-invariant measure $t^{-1}dt$) between the appropriately rescaled process at time $t$ and a standard Gaussian vector.

Our integrability criterion demonstrates why Berry-Esseen bounds have to deteriorate in the limit as $\delta\to0$ when the Levy process is assumed to have $(2+\delta)$ moments. Moreover our criterion shows that in the Non-Normal Gaussian Domain of Attraction, the corresponding convex distance cannot be bounded above by any function integrable at infinity with respect to $t^{-1}dt$.

This is joint work with Jorge Gonz\'alez C\'azares (UNAM) and David Kramer-Bang (Aarhus).

The paper is available on arXiv: https://arxiv.org/abs/2510.06891

The presentation used in this video is here https://drive.google.com/file/d/1_zZl...

More info on my webpage: https://sites.google.com/view/aleks-m...
Warwick webpage: https://warwick.ac.uk/fac/sci/statist...