naa a22 4500 510812058 CHVBK 20180411083447.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1134/S0081543813060126 doi (NATIONALLICENCE)springer-10.1134/S0081543813060126 Weighted moments of the limit of a branching process in a random environment [Elektronische Daten] [Xingang Liang, Quansheng Liu] Let (Z n ) be a supercritical branching process in an independent and identically distributed random environment ζ = (ζ 0, ζ 1, ), and let W be the limit of the normalized population size Z n / $\mathbb{E}$ (Z n |ζ). We show a necessary and sufficient condition for the existence of weighted moments of W of the form $\mathbb{E}$ , where α ≥ 1 and ℓ is a positive function slowly varying at ∞. Pleiades Publishing, Ltd., 2013 Liang Xingang School of Science, Beijing Technology and Business University, 100048, Beijing, China aut Liu Quansheng Laboratoire de Mathématiques de Bretagne Atlantique, UMR 6205, Université de Bretagne-Sud, Campus de Tohannic, BP 573, 56017, Vannes, France aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 127-145 0081-5438 282:1<127 2013 282 11501 https://doi.org/10.1134/S0081543813060126 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813060126 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Liang Xingang School of Science, Beijing Technology and Business University, 100048, Beijing, China aut NATIONALLICENCE 700 1- Liu Quansheng Laboratoire de Mathématiques de Bretagne Atlantique, UMR 6205, Université de Bretagne-Sud, Campus de Tohannic, BP 573, 56017, Vannes, France aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 282/1(2013-10-01), 127-145 0081-5438 282:1<127 2013 282 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer