Survival and extinction : a brief discussion of branching processes

The theory of branching processes is a subfield of probability which tries to answer questions pertaining to the growth and decay of a general population. The purpose of this thesis is fourfold. First, a brief summary of the general theory of the branching process will be given. Second, some examples of branching processes will be given along with their applications. Third, the process of primary interest. the Galton/Watson branching process, will be given a thorough treatment. Fourth and finally, some simulations based on the discussion of the Galton/Watson model will be given, demonstrating the applicability of the developed theory to reality.