Heyde,C.C.(1971): Some central-limit analogues for supercritical branching processes, Journal of Applied Probability, 8, 52-59.  Home/Search   Document Not in Database   Summary   Related Articles

....It follows from the above theorem that, under a finite mean assumption on the offspring distribution function, Z Gamma1 n Z n 1 converges to m( 1) as n 1 w.p.1 on the set of explosion. A central limit theorem for the sequence f Zn 1 Zn ; n 1g is given below (see Athreya [9] and Heyde [40]) Theorem 3. Assume p 0 = 0 and E(Z 2 ffi 1 ) 1. Then q Z n ( Z n 1 Z n Gamma m) d N(0; oe 2 ) where N(0; oe 2 ) is a normal random variable with mean 0 and variance oe 2 . 2 A law of iterated logarithm associated with the above convergence has been established by Heyde [41] ....

Heyde,C.C.(1971): Some central-limit analogues for supercritical branching processes, Journal of Applied Probability, 8, 52-59.

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