caa a22 4500 378915371 CHVBK 20180305123551.0 cr unu---uuuuu 161128e200406 xx s 000 0 eng 10.1515/JAA.2004.83 doi (NATIONALLICENCE)gruyter-10.1515/JAA.2004.83 Becker-Kern P. Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany. email: pbk@math.uni-dortmund.de Random Sums of Independent Random Vectors Attracted by (Semi)-Stable Hemigroups [Elektronische Daten] [P. Becker-Kern] Let (Xn ) be a sequence of independent not necessarily identically distributed random vectors belonging to the domain of attraction of a stable or semistable hemigroup, i.e. for an increasing sampling sequence (kn ) such that k n+1 /kn → c ≥ 1 and linear operators An , the normalized sums converge in distribution uniformly on compact subsets of {0 ≤ s < t} to some full probability μs,t . Suppose that (Tn ) is a sequence of positive integer valued random variables such that Tn/kn converges in probability to some positive random variable, where we do not assume (Xn ) and (Tn ) to be independent. Then weak limit theorems of random sums, where the sampling sequence (kn ) is replaced by random sample sizes (Tn ), are presented. © Heldermann Verlag Random sum nationallicence semistable hemigroup nationallicence random sample size nationallicence Anscombe-condition nationallicence operator selfdecomposability nationallicence random centering nationallicence Journal of Applied Analysis Walter de Gruyter GmbH & Co. KG 10/1(2004-06), 83-104 1425-6908 10:1<83 2004 10 JAA https://doi.org/10.1515/JAA.2004.83 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/JAA.2004.83 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Becker-Kern P. Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany. email: pbk@math.uni-dortmund.de NATIONALLICENCE 773 0- Journal of Applied Analysis Walter de Gruyter GmbH & Co. KG 10/1(2004-06), 83-104 1425-6908 10:1<83 2004 10 JAA CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter