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

• Date: 2006
• Main Authors: Iksanov, O. M., Іксанов, О. М.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3467
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $\mathcal{M}_{(n)},\quad n = 1, 2,...,$ be the supercritical branching random walk in which the family sizes may be infinite with positive probability. Assume that a natural martingale related to $\mathcal{M}_{(n)},$ converges almost surely and in the mean to a random variable $W$. For a large s...