✦ LIBER ✦

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

✍ Scribed by Manuel nindexOrdonezOrdóñez Cabrera; Andrei I. Volodin

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 118 KB
Volume: 55
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(01)00159-6

No coin nor oath required. For personal study only.

✦ Synopsis

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 -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 ÿnite-dimensional space.

📜 SIMILAR VOLUMES

Convergence of randomly weighted sums of

Convergence of randomly weighted sums of Banach-space-valued random elements under some conditions of uniform integrability

✍ M. Ordóñez Cabrera; A. Volodin 📂 Article 📅 2006 🏛 Springer US 🌐 English ⚖ 145 KB

Convergence of randomly weighted sums of

Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights

✍ Tien-Chung Hu; Manuel Ordóñez Cabrera; Andrei I. Volodin 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 115 KB

An application of the Ryll-Nardzewski–Wo

An application of the Ryll-Nardzewski–Woyczyński theorem to a uniform weak law for tail series of weighted sums of random elements in Banach spaces

✍ Tien-Chung Hu; Eunwoo Nam; Andrew Rosalsky; Andrei I. Volodin 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 95 KB

For a sequence of Banach space valued random elements {Vn; n¿1} (which are not necessarily independent) with the series ∞ n = 1 Vn converging unconditionally in probability and an inÿnite array a = {ani; i¿n; n¿1} of constants, conditions are given under which (i) for all n¿1, the sequence of weight

Existence and nonexistence of positive s

Existence and nonexistence of positive solutions for a class of third order BVP with integral boundary conditions in Banach spaces

✍ Junfang Zhao; Peiguang Wang; Weigao Ge 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 264 KB

On the weak law for randomly indexed par

On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces

✍ Dug Hun Hong; Manuel Ordóñez Cabrera; Soo Hak Sung; Andrei I. Volodin 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 104 KB

For weighted randomly indexed sums of the form Nn j = 1 anj(Vnj -cnj) where {anj; j¿1; n¿1} are constants, {Vnj; j¿1; n¿1} are random elements in a real separable martingale type p Banach space, {Nn; n¿1} are positive integer-valued random variables, and {cnj; j¿1; n¿1} are suitable conditional expe

Existence of solutions of boundary value

Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces

✍ Xuemei Zhang; Meiqiang Feng; Weigao Ge 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 709 KB

This paper investigates the existence of solutions for a class of second-order boundaryvalue problems with integral boundary conditions of nonlinear impulsive integrodifferential equations in Banach spaces. The arguments are based upon the fixed point theorem of strict set contraction operators. Mea