Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-16T22:37:45.837Z Has data issue: false hasContentIssue false
  • English
  • Français

On calculating extinction probabilities for branching processes in random environments

Published online by Cambridge University Press:  14 July 2016

William E. Wilkinson
William E. Wilkinson*
Affiliation:
Duke University, Durham, North Carolina
Get access Rights & Permissions [Opens in a new window]

Extract

Consider a discrete time Markov chain {Zn} whose state space is the non-negative integers and whose transition probability matrix ║Pij║ possesses the representation where {Pr}, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z0 = k, a finite positive integer.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 478 - 492
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Gantmacher, F. R. (1959) Applications of the Theory of Matrices. Interscience Publishers, New York.Google Scholar
Hardy, G. H. and Wright, E. M. (1960) An Introduction to the Theory of Numbers. Oxford University Press, London.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Smith, W. L. (1968) Necessary conditions for almost sure extinction of a branching process with random environment. Ann. Math. Statist. 39, 2136–2140.CrossRefGoogle Scholar
Smith, W. L. and Wilkinson, W. E. (1969) On branching processes in random environments. Ann. Math. Statist. 40, 814–827.CrossRefGoogle Scholar