Persistence of heavy-tailed sample averages: principle of infinitely many big jumps (Q2136090)

In this paper the authors study the sample average of a centered random walk in \(\mathbb{R}^d\) with regularly varying step distribution. They show that the tail of the first exit time from a compact convex set not containing the origin is of lognormal type. They also find the typical way for a large exit time to occur.