Limiting distributions for critical multitype branching processes.

T. W. Mullikin

Expert InsightsPublished 1961

A discussion of a multitype branching process for discrete time which is a birth and death process determined by the random variables describing the first generation. The process is critical if the expectation matrix for one generation has its maximum real eigenvalue equal to 1. With probability 1, such a process dies after a finite number of generations. This paper investigates the population size of the nth generation of such a process given that the nth generation is not empty. The results of previous investigations are extended by showing that a certain conditional random variable has a limiting distribution of exponential type. This follows from results about the iterates of a k-dimensional analytic mapping near a fixed point.

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1961
  • Pages: 20
  • Document Number: P-2305

Citation

Chicago Manual of Style

Mullikin, T. W., Limiting distributions for critical multitype branching processes. Santa Monica, CA: RAND Corporation, 1961. https://www.rand.org/pubs/papers/P2305.html.
BibTeX RIS

This publication is part of the RAND paper series. The paper series was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.