Simulation Branching Processes by Mixing Distributions

Limiting Distributions for Branching Processes

Branching Processes with Negative Offspring Distributions

A branching process is a mathematical description of the growth of a population for which the individual produces offsprings according to stochastic laws. Branching processes can be modeled by one-dimensional random walks with non-negative integral step-sizes. In this paper we consider the random walk with a similar algebraic setting but the step-size distribution is allowed to take negative va...

Limiting Distributions for Critical Multitype Branching Processes with Discrete Time(')

Branching Processes

Galton-Watson processes were introduced by Francis Galton in 1889 as a simple mathematical model for the propagation of family names. They were reinvented by Leo Szilard in the late 1930s as models for the proliferation of free neutrons in a nuclear fission reaction. Generalizations of the extinction probability formulas that we shall derive below played a role in the calculation of the critica...

Branching Processes

The study of branching processes began in the 1840s with Irénée-Jules Bienaymé, a probabilist and statistician, and was advanced in the 1870s with the work of Reverend Henry William Watson, a clergyman and mathematician, and Francis Galton, a biometrician. In 1873, Galton sent a problem to the Educational Times regarding the survival of family names. When he did not receive a satisfactory answe...