Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1065-1072.doi: 10.1016/S0252-9602(10)60103-8

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EXTINCTION OF POPULATION-SIZE-DEPENDENT BRANCHING CHAINS IN RANDOM ENVIRONMENTS

 WANG Wei-Gang1, LI Yan2, HU Di-He3   

  • Received:2006-12-21 Revised:2008-10-09 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Research supported by  the National Natural Science Foundation of China  (10771185, 10926036) and Zhejiang Provinicial Natural Science Foundation of China (Y6090172).

Abstract:

We consider a population-size-dependent branching chain in a general random environment.We give sufficident
conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk, θ mk, θ <1, mk, θn1 as k → ∞, n → ∞ , infk, θ mk, θ >1.

Key words: Stochastic population models, branching chains in random environments, extinction probability

CLC Number: 

  • 60F08
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