A branching model{Z n}n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size,but also controlled by a Markovian environmental process{ξn}n≥0.Fo...A branching model{Z n}n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size,but also controlled by a Markovian environmental process{ξn}n≥0.For this model,asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k,θof the offspring distribution converges to m>1 as the population size k grows to∞.In the case that{ξn}n≥0is an irreducible positive recurrent Markov chain,certain extinction(i.e.P(Z n=0 for some n)=1)and noncertain extinction(i.e.P(Z n=0 for some n)<1)are studied.展开更多
基金supported by the Science and Technology Foundation for Developing Colleges and Universities in Shanghai(97A,J06)
文摘A branching model{Z n}n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size,but also controlled by a Markovian environmental process{ξn}n≥0.For this model,asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k,θof the offspring distribution converges to m>1 as the population size k grows to∞.In the case that{ξn}n≥0is an irreducible positive recurrent Markov chain,certain extinction(i.e.P(Z n=0 for some n)=1)and noncertain extinction(i.e.P(Z n=0 for some n)<1)are studied.
