On the weak laws for arrays of random variables

Soo Hak Sung, Tien-Chung Hu and Andrei Volodin

Statistics & Probability Letters, 2005, vol. 72, issue 4, 291-298

Abstract: The convergence in probability of the sequence of sums is obtained, where {un,n[greater-or-equal, slanted]1} and {vn,n[greater-or-equal, slanted]1} are sequences of integers, {Xni,un[less-than-or-equals, slant]i[less-than-or-equals, slant]vn,n[greater-or-equal, slanted]1} are random variables, {cni,un[less-than-or-equals, slant]i[less-than-or-equals, slant]vn,n[greater-or-equal, slanted]1} are constants or conditional expectations, and {bn,n[greater-or-equal, slanted]1} are constants satisfying bn-->[infinity] as n-->[infinity]. The work is proved under a Cesàro-type condition which does not assume the existence of moments of Xni. The current work extends that of Gut (1992, Statist. Probab. Lett. 14, 49-52), Hong and Oh (1995, Statist. Probab. Lett. 22, 52-57), Hong and Lee (1996, Bull. Inst. Math. Acad. Sinica 24, 205-209), and Sung (1998, Statist. Probab. Lett. 38, 10-105).

Keywords: Arrays; Convergence; in; probability; Weak; law; of; large; numbers; Sums; of; random; variables; Martingale; difference; sequence (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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