Acta mathematica scientia, Series B >
LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT
Received date: 2010-12-30
Online published: 2012-05-20
Supported by
Supported by the National Natural Science Foundation of China (10871200).
In this article, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d. random environments.
GAO Zhen-Long , HU Xiao-Yu . LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1193 -1205 . DOI: 10.1016/S0252-9602(12)60091-5
[1] Heyde C C. A rate of convergence result for the supercritical Galton-Watson process. J Appl Prob, 1970, 7(2): 451–454
[2] Heyde C C. Some central limit analogues for the supercritical Galton-Watson process. J Appl Prob, 1971, 8(1): 52–59
[3] Heyde C C. Some almost sure convergence theorems for branching processes. Z W Verw Geb, 1971, 20(1): 189–192
[4] Hu Y L, Yang X Q, Li Y Q. Theorem of equivalence about the branching processes in random environments. Acta Math Appl Sinica, 2007, 30(3): 411–421
[5] Hu D H. The existence and moments of canonical branching chain in random environment. Acta Mathe-matica Scientia, 2004, 24B(3): 499–506
[6] Athreya K B, Karlin S. Branching processes with random environments, I: extinction probabilities. Ann Math Statist, 1971, 42(5): 1499–1520
[7] Athreya K B, Karlin S. Branching processes with random environments, II: limit theorems. Ann Math Statist, 1971, 42(6): 1843–1858
[8] Olav K. Foundations of modern probability. 2rd ed. Beijing: Science Press, 2006
[9] Durrett R. Probability: theorey and examples. Brooks/Cole, 2005
[10] Gao Z L, Hu X Y. Limit theorems for Galton-Watson processes in varying environments (Submitted, 2010)
/
| 〈 |
|
〉 |