ISSN:
1572-9230
Keywords:
Operator semistable laws
;
generalized domains of attraction
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Suppose X, X 1 , X 2 , X 3 ,... are i.i.d. random vectors, and k n a sequence of positive integers tending to infinity in such a way that k n+1 /k n →c≥1. If there exist linear operators A n and constant vectors b n such that $$A_n (X_1 + \cdots + X_{k_n } ) - b_n $$ converges in law to some full limit, then we say that the distribution of X belongs to the generalized domain of semistable attraction of that limit law. The main result of this paper is a decomposition theorem for the norming operators A n , which allows us to reduce the problem to the case where the tail behavior of the limit law is essentially uniform in all radial directions. Applications include a complete description of moments, tails, centering, and convergence criteria.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022638213920
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