Some moment results about the limit of a martingale related to the supercritical branching random walk and perpetuities

• Published in: Український математичний журнал
• Date: 2006
• ISSN: 1027-3190
• Main Author: Iksanov, О.М.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2006
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164970
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Some moment results about the limit of a martingale related to the supercritical branching random walk and perpetuities / О.М. Iksanov // Український математичний журнал. — 2006. — Т. 58, № 4. — С. 451–471. — Бібліогр.: 23 назв. — англ.

Let M(n),n=1,2,..., be the supercritical branching random walk in which the family sizes may be infinite with positive probability. Assume that a natural martingale related to M(n), converges almost surely and in the mean to a random variable W. For a large subclass of nonnegative and concave functi...