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$L^p$-Boundedness of the Overshoot in Multidimensional Renewal Theory
Let $T_r$ be the first time a sum $S_n$ of nondegenerate i.i.d. random variables leaves a ball of radius $r$ in some given norm on $\mathbb{R}^d$. In the case of the Euclidean norm we completely characterize $L^p$-boundedness of the overshoot $\|S_{T_r}\| - r$ in terms of the underlying distribution. For …