Random Sums and Branching Stochastic Processes
Random Sums and Branching Stochastic Processes by Ibrahim Rahimov is a scholarly monograph published by Springer Science & Business Media on January 6, 1995. This softcover reprint of the original first edition spans 195 pages and is presented in English. The book focuses on the application of random sums to analyze the behavior of branching stochastic processes, providing insights and new results applicable to various scenarios.
Readers will find a detailed exploration of how random sums, which involve the summation of a random number of dependent random variables, can be utilized in the study of branching processes. The text addresses processes characterized by reproduction-dependent and non-stationary immigration, offering a straightforward analytical perspective. Additionally, it delves into new characterizations of branching processes without immigration, particularly concerning their genealogical trees. This work is designed for those with a solid foundation in probability and stochastic processes, making it a valuable resource for researchers and graduate students engaged in this field.
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The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
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