Population-size-dependent branching processes in Markovian random environments

查看全文 作　　者：WANG Hanxing 1 and DAI Yonglong 2 1. Department of Mathematics, Shanghai University, Shanghai 201800, China;2. Department of Mathematics, Zhongshan University, Guangzhou 510275, China 出　　处：《Chinese Science Bulletin》索引1998年第43卷第8期,共4页 基　　金：theScienceandTechnologyFoundationforDevelopingCollegesandUniversitiesinShanghai (97AJ0 6 ) 摘　　要：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 {ξ n} 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 {ξ n} 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. 关 键 词：MARKOV CHAINS in RANDOM environments STOCHASTIC POPULATION models branching processes.