منابع مشابه
Branching Random Walk with Catalysts
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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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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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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In the discrete-time branching random walk, the martingale formed by taking the Laplace transform of the nth generation point process is known, for suitable values of the argument, to converge in L 1 under an X log X condition, and to converge to zero when this moment condition fails. This paper examines the strategy used in Biggins and Kyprianou (1996) to prove that, when the X log X condition...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2003
ISSN: 1083-6489
DOI: 10.1214/ejp.v8-127