A weak law for normed weighted sums of random elements in rademacher type p banach spaces

André Adler, Andrew Rosalsky and Robert L. Taylor

Journal of Multivariate Analysis, 1991, vol. 37, issue 2, 259-268

Abstract: For weighted sums [Sigma]j = 1najVj of independent random elements {Vn, n >= 1} in real separable, Rademacher type p (1 p 0 is established, where {vn, n >= 1} and bn --> [infinity] are suitable sequences. It is assumed that {Vn, n >= 1} is stochastically dominated by a random element V, and the hypotheses involve both the behavior of the tail of the distribution of V and the growth behaviors of the constants {an, n >= 1} and {bn, n >= 1}. No assumption is made concerning the existence of expected values or absolute moments of the {Vn, n >- 1}.

Keywords: real; separable; Rademacher; type; p; Banach; space; independent; random; elements; normed; weighted; sums; weak; law; of; large; numbers; convergence; in; probability; stochastically; dominated; random; elements (search for similar items in EconPapers)
Date: 1991
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