Necessary and sufficient condition for M₂-convergence to a Lévy process for billiards with cusps at flat points.

Stoch. Dyn. 21 (2021) 2150024, 8 pages.

Paul Jung, Ian Melbourne, Françoise Pène, Paulo Varandas and Hong-Kun Zhang

Abstract

We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding Lévy process in the M₁ and M₂ Skorohod topologies has been studied in recent work. Here we show that certain sufficient conditions for M₂-convergence are also necessary.