Random Sums and Branching Stochastic Processes

1. Front Matter

   Pages i-ix

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2. Introduction

   • Ibrahim Rahimov

   Pages 1-4

3. Sums of a Random Number of Random Variables

   • Ibrahim Rahimov

   Pages 5-43

4. Branching Processes with Generalized Immigration

   • Ibrahim Rahimov

   Pages 44-104

5. Branching Processes with Time-Dependent Immigration

   • Ibrahim Rahimov

   Pages 105-155

6. The Asymptotic Behavior of Families of Particles in the Branching Process

   • Ibrahim Rahimov

   Pages 156-184

7. Back Matter

   Pages 185-195

   PDF

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.

• Branching process
• Random variable
• Stochastic processes
• Variance
• stochastic process

• The Institute of Mathematics, The Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan

  Ibrahim Rahimov

• Department of Statistics, Middle East Technical University, Ankara, Turkey

  Ibrahim Rahimov

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