Article ID Journal Published Year Pages File Type
1154675 Statistics & Probability Letters 2006 5 Pages PDF
Abstract
We link the infinitely divisible measure μ to its modified Lévy measure ρ=ρ(μ) in terms of their variance functions, where x-2[ρ(dx)-ρ({0})δ0(dx)] is the Lévy measure associated with μ. We deduce that, if the variance function of μ is a polynomial of degree p⩾2, then, the variance function of ρ is still a second degree polynomial. We illustrate these results with some Lévy processes such as positive stable and a class of Poisson stopped-sum processes.
Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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