A class of two-sex branching processes with reproduction phase in a random environment. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Ma, S.; Molina, M.; Xing, Y.
• Is Part Of: Stochastics. Volume 88:Issue 1(2016)
• Page Start: 147
• Page End: 161
• Publication Date: 2016-01-02
• Subjects: branching process -- two-sex process -- process in a random environment -- extinction probability -- asymptotic behaviour; 60J80 -- 60K37; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2015.1044532
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : We model the demographic dynamics of populations with sexual reproduction where the reproduction phase occurs in a non-predictable environment and we assume the immigration/out-migration of mating units in the population. We introduce a general class of two-sex branching processes where, in each generation, the number of mating units which take part in the reproduction phase is randomly determined and the offspring probability distribution changes over time in a random environment. We provide several probabilistic results about the limit behaviour of populations whose dynamics is modelled by such a class of stochastic processes. In particular, we provide sufficient conditions for the almost sure extinction of the population or for its survival with a positive probability. As illustration, we include some simulated examples.