On the multi-dimensional renewal theorem |
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Authors: | Hasse Carlsson Stephen Wainger |
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Institution: | Department of Mathematics, University of Göteborg, S-412 96 Göteborg, Sweden;Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 U.S.A. |
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Abstract: | Let X be a random variable on Rn, n ? 2, having a density. Assume X has a finite exponential moment and non-zero mean vector, μ. Let ν be the corresponding renewal measure, and Q a cube. We obtain an asymptotic formula for ν(x + Q) as x → ∞ which is uniform in a small cone about the mean vector. This formula depends on moments of arbitrarily high order but depends only on the first and second moments of X in a region . |
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