Convergence in the pth-mean and some Weak Laws of Large Numbers for weighted sums of random elements in separable normed linear spaces

Xiang Chen Wang and M. Bhaskara Rao

Journal of Multivariate Analysis, 1984, vol. 15, issue 1, 124-134

Abstract: . Let Xn, n >= 1, be a sequence of tight random elements taking values in a separable Banach space B such that Xn, n >= 1, is uniformly integrable. Let ank, n >= 1, k >= 1, be a double array of real numbers satisfying [Sigma]k >= 1 ank = 1 for some positive constant [Gamma]. Then [Sigma]k >= 1 ankXk, n >= 1, converges to 0 in probability if and only if [Sigma]k >= 1 ankf(Xk), n >= 1, converges to 0 in probability for every f in the dual space B*.

Keywords: Random; elements; convergence; in; probability; convergence; in; the; pth-mean; separable; Banach; space; dual; space; total; set; weak*-topology; tightness; weighted; sums; uniform; integrability (search for similar items in EconPapers)
Date: 1984
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