S. Asmussen, Almost sure behavior of linear functionals of supercritical branching processes. Trans. Amer. Math. Soc. 231 (1977), no. 1, 233--248.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....too by the methods of this paper, first considering the corresponding continuous time model, but we have not pursued this. This case is substantially more complicated than the standard case treated here; for example, the continuous time model will explode in finite time. Remark 4.6. Asmussen [3] has proved laws of iterated logarithm for (t) in the irreducible case. The results in the cases Re# 2 Re# 1 and Re# 2 = Re# 1 are di#erent. By the Athreya Karlin embedding, this yields laws of iterated logarithm for the urn process X n complementing the results above; we leave the ....

S. Asmussen, Almost sure behavior of linear functionals of supercritical branching processes. Trans. Amer. Math. Soc. 231 (1977), no. 1, 233--248.

....u DeltaZ n ) d Gamma N(0; oe 2 ) for some 0 oe 2 1 independent of Z 0 . 2 There are extensions of this result to arbitrary vectors l (see Athreya [10 ] and Athreya and Ney [23] Further limit results for functionals of branching process have been established in Asmussesn (see [1] [2], and [3] Asmussen and Keiding [7] and Asmussen and Kurtz [8] The large deviation results for multitype branching processes have been considered by Athreya and Vidyashankar (see [25] and [26] This leads to interesting questions about the rates of decay of iterates of multidimensional ....

Asmussen,S.(1977): Almost sure behavior of linear functionals of supercritical branching processes, Transactions of American Mathematical Society, 1, 233-248.

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