Titlebook: Classical and Modern Branching Processes; Krishna B. Athreya,Peter Jagers Book 1997 Springer Science+Business Media New York 1997 Branchin

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Incidence and Arrangement Problems,alks with drift: e.g., is the speed on Galton-Watson trees monotonic in the drift parameter? These random walks have been used in Monte-Carlo algorithms for sampling from the vertices of a tree; in general, their behavior reflects the size and regularity of the underlying tree. Random walks are rela

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Stochastic Monotonicity and Branching Processes,o con­vergence in probability or a.s. of suitably normed branching processes is a law of large numbers for some independent copies of random variables. Applications to branching processes in varying environment are given.

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A Criterion of Boundedness of Discrete Branching Random Walk,on of a parent. A necessary and sufficient condition is given for the random variable.to be finite. Here .. is the position of the k-th offspring in the n-th generation. The condition is stated in terms of a naturally arising linear functional equation. A number of examples are discussed, where the condition may be verified.

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A Standard for Test and Diagnosis,nsions are discussed. The relationship of the results with deterministic theory is also indicated. Finally the theory developed is used to re-prove smoothly (and improve slightly) results on certain data-storage algorithms arising in computer science.