A SURVEY OF BRANCHING PROCESSES

Abstract

A mathematical model of a branching process utilizing generating functions is presented. The probability distribution of the number of members of the process at discrete time periods, Z (sub N) and the probability of extinction is discussed. When there is a non-zero probability of surviving indefinitely, the normed random variables Z (sub N)/E (sub N) converge with probability one; the cumulative distribution of this random variable is absolutely continuous. The time until extinction and the total number of members of the process is examined when the probability of extinction is one. The distribution of the Z (sub N) given that Z (sub N) is not zero is discussed for this case. The maximum likelihood estimates for the probabilities involved in the process are determined. An example is given of a branching process in which the probabilities are dependent on time and a solution is found using Laplace transform methods.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1963
Accession Number
AD0482320

Entities

People

  • John B. Shewmaker

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • California
  • Collisions
  • Complex Variables
  • Electrons
  • Equations
  • Integrals
  • Ionization
  • Kolmogorov Equations
  • Markov Processes
  • Mathematical Models
  • Models
  • Power Series
  • Probability
  • Probability Distributions
  • Random Variables
  • Stochastic Processes
  • United States

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Approximation Theory.
  • Statistical inference.