Journal of University of Chinese Academy of Sciences >
P-convergence of a double sequence of random variables
Received date: 2015-07-08
Revised date: 2016-03-24
Online published: 2016-09-15
In this study we investigate the P-convergence of random sum(say ξn) of a double random sequence of random variables {Xn,i:n≥1,i≥1} in two cases. The first case is that {ξn:n≥1} is independent of Xn,i:n≥1,i≥1},and the second case is that {ξn:n≥1} is not necessarily independent of the double sequence {Xn,i:n≥1,i≥1}.These results include P-convergence of a branching process in varying environments.
ZHANG Zhiyang , HU Xiaoyu . P-convergence of a double sequence of random variables[J]. Journal of University of Chinese Academy of Sciences, 2016 , 33(5) : 590 -595 . DOI: 10.7523/j.issn.2095-6134.2016.05.003
[1] Gendenko B V, Kolmogorov A N. Limit distributions for sums of independent random variables[M]. Chung K L,trans. Cambridge:Addison-Wesley, 1954.
[2] Tucker H G. A graduate course in probability[M]. New York and London:Academic Press, 1967.
[3] 胡迪鹤. 不变原理及其在分枝过程中的应用[J]. 北京大学学报:自然科学版,1964,(1):1-27.
[4] Heyde C C. Some central limit analogues for supercritical Galton-Watson processes[J]. Appl Prob, 1971, 8(1):52-59.
[5] 高振龙. 随机环境中Galton-Watson分枝过程的极限定理[D]. 北京:中国科学院研究生院, 2011.
[6] Gao Z L, Hu X Y. Limit theorems for a Galton-Watson process in the i.i.d. random environment[J]. Acta Mathematica Scientia, 2012, 32(3):1193-1205.
[7] 胡迪鹤. 分析概率论[M]. 北京:科学出版社,1997.
[8] Athreya K B, Ney P E. Branching processes[M]. Berlin, Heidelberg, New York:Springer-Verlag, 1972.
/
| 〈 |
|
〉 |