Evolution of branching processes in a random environment
Journal article, 2013

This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in independent and identically distributed random environments. This is a natural generalization of the time-inhomogeneous branching processes. The key assumptions of the family of population models in question are nonoverlapping generations and discrete time. The reader should be aware of the fact that there are many very interesting papers covering other issues in the theory of branching processes in random environments which are not mentioned here.

survival probability

galton-watson processes

extinction

random-walks

limit-theorems

Author

Fima C. Klebaner

Russian Academy of Sciences

E. Dyakonova

Russian Academy of Sciences

Serik Sagitov

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

Proceedings of the Steklov Institute of Mathematics

0081-5438 (ISSN)

Vol. 282 1 220-242

Stochastic models of gene and species trees

Swedish Research Council (VR), 2011-01-01 -- 2013-12-31.

Subject Categories

Mathematics

DOI

10.1134/s0081543813060187

More information

Latest update

4/16/2018