Limiting Distributions For Critical Multitype Branching Processes With Discrete Time

Limiting Distributions for Critical Multitype Branching Processes

Limiting Distributions for Critical Multitype Branching Processes with Discrete Time

The theory of branching processes treats the multiplication of objects subject to laws of chance. It has been applied to such phenomena as bacterial fission, cosmic ray showers, and neutron chain reactions. This report describes the probability law governing the descendants of a single object after many generations, if on the average an object has just one surviving child (in the language of reactors, this is the critical case). These results could be useful in the study of controlled nuclear reactions. (Author).

Discrete Time Branching Processes in Random Environment

Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.