Article ID Journal Published Year Pages File Type
1153749 Statistics & Probability Letters 2007 13 Pages PDF
Abstract
Let {X1,X2,…} be a sequence of independent and identically distributed positive random variables of Pareto-type and let {N(t);t⩾0} be a mixed Poisson process independent of the Xi's. For any fixed t⩾0, define:TN(t)≔X12+X22+⋯+XN(t)2(X1+X2+⋯+XN(t))2if N(t)⩾1 and TN(t)≔0 otherwise. We determine the asymptotic behavior of any moment E[TN(t)k] as t→∞ with k∈N. Our method relies on the theory of functions of regular variation and an integral representation of these moments.
Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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