Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability. (English) Zbl 1065.60022

Ordóñez Cabrera, Manuel; Volodin, Andrei I.

J. Math. Anal. Appl. 305, No. 2, 644-658 (2005).

A new concept of integrability, called \(h\)-integrability, is introduced and, under this condition, mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables are obtained.

Reviewer: George Stoica (Saint John)

MSC:

60F05	Central limit and other weak theorems
60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)

Keywords:

Uniform integrability; Weighted sums; Integrability concerning the weights; Negative dependence; Non-positive correlation; \(\varphi\)-Mixing sequence; Random elements; Martingale type Banach space

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