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Necessary and sufficient condition for ℳ2-convergence to a Lévy process for billiards with cusps at flat points
Stochastics and Dynamics  (IF0.98),  Pub Date : 2020-09-04, DOI: 10.1142/s0219493721500246
Paul Jung, Ian Melbourne, Françoise Pène, Paulo Varandas, Hong-Kun Zhang

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.