关键词: 二重序列随机和, 分枝过程, P-收敛

Abstract:

In this study we investigate the P-convergence of random sum(say ξ_n) of a double random sequence of random variables {X_n,i:n≥1,i≥1} in two cases. The first case is that {ξ_n:n≥1} is independent of X_n,i:n≥1,i≥1},and the second case is that {ξ_n:n≥1} is not necessarily independent of the double sequence {X_n,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