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.

中文翻译：

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平点台球 ℳ2-收敛到 Lévy 过程的充要条件

我们考虑一类平面分散台球，其尖端在曲率消失的点。收敛到一个稳定的定律和相应的 Lévy 过程ℳ1和ℳ2在最近的工作中研究了 Skorohod 拓扑。在这里，我们证明了某些充分条件ℳ2-收敛也是必要的。