Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1153749 | Statistics & Probability Letters | 2007 | 13 Pages |
Abstract
Let {X1,X2,â¦} 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)âX12+X22+â¯+XN(t)2(X1+X2+â¯+XN(t))2if N(t)⩾1 and TN(t)â0 otherwise. We determine the asymptotic behavior of any moment E[TN(t)k] as tââ with kâN. Our method relies on the theory of functions of regular variation and an integral representation of these moments.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Sophie A. Ladoucette,