Bounds For Subcritical BPRE

Firstly, in this paper some elementary theories about GW branching processes, some primary conclusions about subcritical branching processes are introduced. On these foundations, through using the elementary theories and method for example as limit, derivative, Taylor formula and so on in the higher mathematics, the decision theorem about that a subcritical branching process is certainly extinct or not is proved.Secondly,Kolmogorov(1938) showed for subcritical G-W branching processes, if E(z₁²)<∞, then:Heathcote and senete(1966) have obtained bounds for c .But in the arguments by which these bounds are derived, it is only assumed that the first two moments of the distribution of offspring exit. We will assume that the first three moments exist, and...