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.

1. Branching Processes in Varying Environment.
2. Branching Processes in Random Environment.
3. Large Deviations for BPREs.
4. Properties of Random Walks.
5. Critical BPREs: the Annealed Approach.
6. Critical BPREs: the Quenched Approach.
7. Weakly Subcritical BPREs.
8. Intermediate Subcritical BPREs.
9. Strongly Subcritical BPREs.
10. Multi-type BPREs. 

Vladimir Vatutin, Steklov Mathematical Institute, Russia.