Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590842 | Journal of Functional Analysis | 2012 | 24 Pages |
Abstract
We introduce the notion of strict domain of attraction in the context of monotone probability theory and prove that a law has a nonempty strict domain of attraction if and only if it is strictly stable. We also show that the monotonic weak law of large numbers is equivalent to the classical and the free weak laws of large numbers. Finally, a necessary condition for a measure μ to belong to the strict domain of attraction of a nondegenerate strictly stable law is given in terms of the absolute moments of μ.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory