Total progeny in killed branching random walk
نویسندگان
چکیده
منابع مشابه
Total Progeny in Killed Branching Random Walk
We consider a branching random walk for which the maximum position of a particle in the n’th generation, Rn, has zero speed on the linear scale: Rn/n → 0 as n → ∞. We further remove (“kill”) any particle whose displacement is negative, together with its entire descendence. The size Z of the set of un-killed particles is almost surely finite [26, 31]. In this paper, we confirm a conjecture of Al...
متن کاملTail Asymptotics for the Total Progeny of the Criti- Cal Killed Branching Random Walk
We look at the branching random walk on R+ killed below zero. Let b ≥ 2 be a deterministic integer which represents the number of children of the branching random walk, and x ≥ 0 be the position of the (unique) ancestor. We introduce the rooted b-ary tree T , and we attach at every vertex u except the root an independent random variable Xu picked from a common distribution (we denote by X a gen...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملBranching random walk in Z with branching
For the critical branching random walk in Z 4 with branching at the origin only we find the asymptotic behavior of the probability of the event that there are particles at the origin at moment t → ∞ and prove a Yaglom type conditional limit theorem for the number of individuals at the origin given that there are particles at the origin.
متن کاملAsymptotics for the survival probability in a killed branching random walk
Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope γ − ε, where γ denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2010
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-010-0299-2