Franke, BriceWendler, Martin2012-12-172012-12-172012-12-17http://hdl.handle.net/2003/2983010.17877/DE290R-10365Let (Sn)n2N be a random walk in the domain of attraction of an a -stable Lévy process and ( (n))n2N a sequence of iid random variables (called scenery). We want to investigate U-statistics indexed by the random walk Sn, that is Un := P 1 i<j n h( (Si); (Sj )) 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 Un.enDiscussion Paper / SFB 823;57/2012law of the iterated logarithmrandom sceneryrandom walkstable limitsU-statistics310330620working paper