Asymptotic behavior of the moments of the ratio of the random sum of squares to the square of the random sum

Sophie A. Ladoucette

Statistics & Probability Letters, 2007, vol. 77, issue 10, 1021-1033

Abstract: Let {X1,X2,...} be a sequence of independent and identically distributed positive random variables of Pareto-type and let be a mixed Poisson process independent of the Xi's. For any fixed t[greater-or-equal, slanted]0, define:if N(t)[greater-or-equal, slanted]1 and TN(t):=0 otherwise. We determine the asymptotic behavior of any moment as t-->[infinity] with . Our method relies on the theory of functions of regular variation and an integral representation of these moments.

Keywords: Convergence; of; moments; Functions; of; regular; variation; Laplace; transform; Mixed; Poisson; process; Pareto-type; distribution; Risk; measures (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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