Almost sure limit sets of random samples in ℝd
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If {Xj, } is a sequence of i.i.d. random vectors in , when do there exist scaling constants bn > 0 such that the sequence of random sets converges almost surely in the space of compact subsets of to a limit set? A multivariate regular variation condition on a properly defined distribution tail guarantees the almost sure convergence but without certain regularity conditions surprises can occur. When a density exists, an exponential form of regular variation plus some regularity guarantees the convergence.
2009 ◽
Vol 147
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pp. 455-488
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2019 ◽
Vol 2019
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pp. 149-170
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2019 ◽
Vol 173
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pp. 525-550
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1995 ◽
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pp. 19-32
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1996 ◽
Vol 28
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pp. 384-393
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Vol 21
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pp. 3205-3215
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pp. 139-163
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Vol 28
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pp. 1177-1195
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