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›› 2016, Vol. 33 ›› Issue (5): 590-595.DOI: 10.7523/j.issn.2095-6134.2016.05.003

• Research Articles • Previous Articles     Next Articles

P-convergence of a double sequence of random variables

ZHANG Zhiyang, HU Xiaoyu   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2015-07-08 Revised:2016-03-24 Online:2016-09-15

Abstract:

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.

Key words: random sum of a double random sequence of random variables, branching process, P-convergence

CLC Number: