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引用次数: 4
摘要
摘要考虑由独立同分布变量构成的随机环境中分支过程Zn的大偏差概率。假设关联随机游走Sn = ξ1 +…+ ξn有一个有限均值μ,且满足cramsamir条件E ehξi <∞,0 < h < h+。在Z1的附加矩约束下,对于值x/n在取决于过程类型的范围内变化,以及对于所有在n→∞时足够缓慢地趋于零的序列Δn,找到了概率P (ln Zn∈[x, x + Δn))的确切渐近。对于随机环境下的随机过程,也证明了一个类似的定理。
Large deviations of branching process in a random environment. II
Abstract We consider the probabilities of large deviations for the branching process Zn in a random environment, which is formed by independent identically distributed variables. It is assumed that the associated random walk Sn = ξ1 + … + ξn has a finite mean μ and satisfies the Cramér condition E ehξi < ∞, 0 < h < h+. Under additional moment constraints on Z1, the exact asymptotic of the probabilities P (ln Zn ∈ [x, x + Δn)) is found for the values x/n varying in the range depending on the type of process, and for all sequences Δn that tend to zero sufficiently slowly as n → ∞. A similar theorem is proved for a random process in a random environment with immigration.
期刊介绍:
The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.