On the rate of convergence of a regular martingale related to the branching random walk
| dc.creator | Iksanov, Aleksander | |
| dc.date | 2006-04-20 | |
| dc.date.accessioned | 2026-07-07T07:11:07Z | |
| dc.date.available | 2026-07-07T07:11:07Z | |
| dc.description | Let $\mm_n, n=0,1,...$ be the supercritical branching random walk, in which the number of direct descendants of one individual may be infinite with positive probability. Assume that the standard martingale $W_n$ related to $\mm_n$ is regular, and $W$ is a limit random variable. Let $a(x)$ be a nonnegative function which regularly varies at infinity, with exponent greater than -1. The paper presents sufficient conditions of the almost sure convergence of the series $\sum_{n=1}^{\infty}a(n)(W-W_n)$. Also we establish a criterion of finiteness of $\me W\log^+ W a(\log^+W)$ and $\me \log^+|\zi| a(\log^+|\zi|)$, where $\zi:=Q_1+\sum_{n=2}^\infty M_1... M_n Q_{n+1}$, and $(M_n, Q_n)$ are independent identically distributed random vectors, not necessarily related to $\mm_n$. | |
| dc.identifier | https://arxiv.org/abs/math/0604440 | |
| dc.identifier | http://arxiv.org/abs/math/0604440 | |
| dc.identifier | The original, Ukrainian variant of the paper was published in Ukrainian Mathematical Journal (2006), 58(3), 326-342 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111635 | |
| dc.subject | Probability | |
| dc.subject | Primary: 60J80, 60E99 ; Secondary: 60G50 | |
| dc.title | On the rate of convergence of a regular martingale related to the branching random walk | |
| dc.type | text |