7 papers
Infinite-variation Lévy processes are either strongly eroded or abrupt
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We prove that every real Lévy process of infinite variation is either abrupt or strongly eroded, resolving the conjectured geometric dichotomy on the smoothness of the convex hull…
Generalised Random Parking for Trapeziums on a Strip
David Kramer-Bang, Stjepan Šebek
In this article, we study a generalisation of Rényi's car-parking problem in which isosceles trapeziums are sequentially deposited on a strip. We derive an explicit formula for the…
Improved bounds on the inradius and inverse inradius process of the convex hull of planar Brownian motion
David Kramer-Bang, Hugo Panzo, Stjepan Šebek
We study the inradius and inverse inradius of the convex hull of standard planar Brownian motion. Our main goals are to improve the existing bounds on the expected values of these…
Multivariate CLT for Lévy processes: convergence rates without moment assumptions
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We prove that the norm of a -dimensional Lévy process possesses a finite second moment if and only if the convex distance between an appropriately rescaled process at time a…
Rates of convergence for multivariate SDEs driven by Lévy processes in the small-time stable domain of attraction
Jorge González Cázares, David Kramer-Bang
This paper explores the rates of convergence of solutions for multivariate stochastic differential equations (SDEs) driven by Lévy processes within the small-time stable domain of…
Asymptotically optimal Wasserstein couplings for the small-time stable domain of attraction
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We develop two novel couplings between general pure-jump Lévy processes in and apply them to obtain upper bounds on the rate of convergence in an appropriate Wasserstein dis…
Hölder continuity of the convex minorant of a Lévy process
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We characterise the Hölder continuity of the convex minorant of most Lévy processes. The proof is based on a novel connection between the path properties of the Lévy process at zer…