A NOTE ON BISEXUAL GALTON-WATSON BRANCHING PROCESSES IN RANDOM ENVIRONMENTS

• Fernández-Ponce José María

  Universidad de Sevilla

• Ortega Eva María

  Universidad Miguel Hernández

• Pellerey Franco

Abstract

A bisexual Galton-Watson branching process is a two–type branching model, in which matings in one generation give rise to random numbers of both males and females in the next. The mating function describes how many mating units are formed from given numbers of males and females. In this paper we consider the case that the distributions of the random numbers of males and females produced by the mating units depend on some fertility parameters evolving randomly in time. By means of a main stochastic comparison result, we show that the total population increases, in some stochastic sense, as the positive dependence between the fertility indexes increases. Simple examples of applications of this result are provided, together with other similar results for a different model of population growth.

Journal

• Scientiae Mathematicae Japonicae

  Scientiae Mathematicae Japonicae 67 (2), 291-304, 2008

  International Society for Mathematical Sciences

Keywords

• Increasing convex order
• increasing directionally convex order
• stochastically increasing and directionally convex property (in the sample path sense)
• branching processes
• shock models
• immigration models
• random environments

Details

• CRID: 1390283659856904320
• NII Article ID: 10021089599
• NII Book ID: AA1150654X
• DOI: 10.32219/isms.67.2_291
• ISSN: 13460447
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed