منابع مشابه
Central 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.
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Abstract Shnerb et al. (2000), (2001) studied the following system of interacting particles on Z: There are two kinds of particles, called A-particles and B-particles. The A-particles perform continuous time simple random walks, independently of each other. The jumprate of each A-particle is DA. The B-particles perform continuous time simple random walks with jumprate DB , but in addition they ...
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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...
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Consider a particle that can replicate itself instantaneously at random times. In general there is a distribution of times from which the particle draws in order to initiate replication. For simplicity, we assume a Poisson process, and a replication rate of λ. Consider the total integer number of particles N(t) at any time t. Let us now consider one realization of the continuous-time branching ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0370775-4