Semi-attraction domains of semistable laws on topological vector spaces
Let E be a locally convex topological vector space. Moreover let p and q be Radon measures on E such that q is convexly tight; and let p belong to the domain of partial attraction of q with respect to a strictly increasing sequence \((n_ k)_{k\geq 1}\) of integers. The main part of this paper is dedicated to the following two theorems: 1. If the sequence \((n_ k/n_{k+1})_{k\geq 1}\) admits an accumulation point in (0,1) then q is semistable. 2. If lim inf \(n_ k/n_{k+1}\) is positive and if q is r-semistable (resp. stable) then p belongs to the domain of r-semi-attraction (resp. to the domain of attraction) of q. These results permit less restrictive definitions of ``semistability'' and of ``domain of semi-attraction''. The proofs are based on a paper by \textit{D. M. Chung}, \textit{B. S. Rajput} and \textit{A. Tortrat} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 60, 209-218 (1982; Zbl 0468.60006)].
scientific article; zbMATH DE number 4111666