On conditional compactly uniform pth-order integrability of random elements in Banach spaces

Manuel Ordóñez Cabrera and Andrei I. Volodin

Statistics & Probability Letters, 2001, vol. 55, issue 3, 301-309

Abstract: The notion of conditional compactly uniform pth-order integrability of an array of random elements in a separable Banach space concerning an array of random variables and relative to a sequence of [sigma]-algebras is introduced and characterized. We state a conditional law for randomly weighted sums of random elements in a Banach space with the bounded approximation property, and we prove that, under the introduced condition, the problem can be reduced to a similar problem for random elements in a finite-dimensional space.

Keywords: Random; elements; Randomly; weighted; sums; Conditional; compactly; uniform; pth-order; integrability; Conditional; tightness; Conditional; uniform; integrability; Bounded; approximation; property; Schauder; basis (search for similar items in EconPapers)
Date: 2001
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