New Preprint: Stable Limit Theorem for U-Statistic Processes Indexed by a Random Walk

A new preprint joint with Brice Franke about „Stable Limit Theorem for U-Statistic Processes Indexed by a Random Walk“ is online at arXiv.

Abstract: Let (S_n)_{n\in\N} be a random walk in the domain of attraction of an α-stable Lévy process and (\xi(n))_{n\in\N} a sequence of iid random variables (called scenery). We want to investigate U-statistics indexed by the random walk S_n, that is U_n:=\sum_{1\leq i< j\leq n}h(\xi(S_i),\xi(S_j)) for some symmetric bivariate function h. We will prove the weak convergence without the assumption of finite variance. Additionally, under the assumption of finite moments of order greater than two, we will establish a law of the iterated logarithm for the U-statistic U_n.